Quantum mechanics is a first quantized quantum theory that supersedes classical mechanics at the atomic and subatomic levels. It is a fundamental branch of physics that provides the underlying mathematical framework for many fields of physics and chemistry.
A - B
- So, what is quantum mechanics? Even though it was discovered by physicists, it’s not a physical theory in the same sense as electromagnetism or general relativity. In the usual “hierarchy of sciences” – with biology at the top, then chemistry, then physics, then math – quantum mechanics sits at a level between math and physics that I don’t know a good name for. Basically, quantum mechanics is the operating system that other physical theories run on as application software (with the exception of general relativity, which hasn’t yet been successfully ported to this particular OS). There’s even a word for taking a physical theory and porting it to this OS: “to quantize.”
- Scott Aaronson, Quantum Computing Since Democritus (2013), Ch. 9 : Quantum
- Quantum mechanics was, and continues to be, revolutionary, primarily because it demands the introduction of radically new concepts to better describe the world. In addition we have argued that conceptual quantum revolutions in turn enable technological quantum revolutions.
- Alain Aspect, "Introduction: John Bell and the second quantum revolution", in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (2nd ed, 2004)
- No other theory of the physical world has caused such consternation as quantum theory, for no other theory has so completely overthrown the previously cherished concepts of classical physics and our everyday apprehension of reality. For philosophers, it has been a romping ground of epistemological adventure of pessimism about science's ability to expose ultimate truth. For physicists, it has required a confrontation with the nature of physical reality and a heady inhalation of new attitudes. For all scientists and technologists, it has been the key to advances in all fields of endeavor, from genetics to superconductivity.
The extraordinary feature of quantum theory is that although we do not understand it, we can apply the rules of calculation it inspires, and compute properties of matter to unparalleled accuracy, in some cases with a precision that exceeds that currently obtained from experiment.
- … that what is proved, by impossibility proofs, is lack of imagination.
- John S. Bell, On the impossible pilot wave, Ref.TH.3315-CERN, 1982, p. 15
- I am a Quantum Engineer, but on Sundays I Have Principles.
- Quantum mechanics had never been wrong. And now we know that it will not be wrong even in these very tricky conditions.
- John S. Bell, interview in The Ghost in the Atom: A Discussion of the Mysteries of Quantum Physics (1986) edited by P. C. W. Davies and Julian R. Brown
- I'm quite convinced of that: quantum theory is only a temporary expedient.
- John S. Bell, interview in The Ghost in the Atom: A Discussion of the Mysteries of Quantum Physics (1986) edited by P. C. W. Davies and Julian R. Brown
- I hesitated to think it might be wrong, but I knew that it was rotten. That is to say, one has to find some decent way of expressing whatever truth there is in it.
- The entire universe must, on a very accurate level, be regarded as a single indivisible unit in which separate parts appear as idealisations permissible only on a classical level of accuracy of description. This means that the view of the world being analogous to a huge machine, the predominant view from the sixteenth to nineteenth centuries, is now shown to be only approximately correct. The underlying structure of matter, however, is not mechanical. This means that the term "quantum mechanics" is very much a misnomer. It should, perhaps, be called "quantum nonmechanics".
- David Bohm, Quantum Theory (1951)
- For those who are not shocked when they first come across quantum theory cannot possibly have understood it.
- Niels Bohr, in 1952, quoted in Heisenberg, Werner (1971). Physics and Beyond. New York: Harper and Row. pp. 206.
- If relativity is about the geometrical structure of space-time, what is quantum mechanics about? There are a surprising variety of answers to this question: that quantum mechanics is about energy being quantized in discrete lumps or quanta, or about particles being wavelike, or about the universe continually splitting into countless co-existing quasi-classical universes, with many copies of ourselves, and so on. A rather more mundane answer, with quite remarkable implications, has emerged over the past thirty years or so from the study of the difference between classical information and quantum information: quantum mechanics is about new sorts of probabilistic correlations in nature, so about the structure of information, insofar as a theory of information in the sense relevant to physics is essentially a theory of probabilistic correlations.
- Jeffrey Bub, Bananaworld: Quantum Mechanics for Primates (2015), Ch. 1 : Nobody Understands Quantum Mechanics
C - D
- The power of the new quantum mechanics in giving us a better understanding of events on an atomic scale is becoming increasingly evident. The structure of the helium atom, the existence of half-quantum numbers in band spectra, the continuous spatial distribution of photo-electrons, and the phenomenon of radioactive disintegration, to mention only a few examples, are achievements of the new theory which had baffled the old.
- Arthur Compton, Foreword to the English edition of The Physical Principles of the Quantum Theory by W. Heisenberg (1930)
- Already in 1948, observations... agreed with quantum mechanics, not with local realism.
- Classical mechanics has been developed continuously from the time of Newton and applied to an ever-widening range of dynamical systems, including the electromagnetic field in interaction with matter. The underlying ideas and the laws governing their application form a simple and elegant scheme, which one would be inclined to think could not be seriously modified without having all its attractive features spout. Nevertheless it has been found possible to set up a new scheme, called quantum mechanics, which is more suitable for the description of phenomena on the atomic scale and which is in some respects more elegant and satisfying than the classical scheme. This possibility is due to the changes which the new scheme involves being of a very profound character and not clashing with the features of the classical theory that make it so attractive, as a result of which all these features can be incorporated in the new scheme.
- P. A. M. Dirac, The Principles of Quantum Mechanics (4th ed., 1958), I. The Principle of Superposition - 1. The need for a quantum theory
- I have observed in teaching quantum mechanics, and also in learning it, that students go through an experience similar to the one that Pupin describes. The student begins by learning the tricks of the trade. He learns how to make calculations in quantum mechanics and get the right answers, how to calculate the scattering of neutrons by protons and so forth. To learn the mathematics of the subject and to learn how to use it takes about six months. This is the first stage in learning quantum mechanics, and it is comparatively painless. The second stage comes when the student begins to worry because he does not understand what he has been doing. He worries because he has no clear physical picture in his head. He gets confused in trying to arrive at a physical explanation for each of the mathematical tricks he has been taught. He works very hard and gets discouraged because he does not seem to be able to think clearly. This second stage often lasts six months or longer. It is strenuous and unpleasant. Then, unexpectedly, the third stage begins. The student suddenly says to himself, “I understand quantum mechanics,” or rather he says, “I understand now that there isn’t anything to be understood.” The difficulties which seemed so formidable have mysteriously vanished. What has happened is that he has learned to think directly and unconsciously in quantum-mechanical language. He is no longer trying to explain everything in terms of prequantum conceptions.
The duration and severity of the second stage are decreasing as the years go by. Each new generation of students learns quantum mechanics more easily than their teachers learned it. The students are growing more detached from prequantum pictures. There is less resistance to be broken down before they feel at home with quantum ideas. Ultimately, the second stage will disappear entirely. Quantum mechanics will be accepted by students from the beginning as a simple and natural way of thinking, because we shall all have grown used to it. By that time, if science progresses as we hope, we shall be ready for the next big jump into the unknown.
- Freeman Dyson, "Innovation in Physics", Scientific American (1958), published in From Eros to Gaia
- For me, the important thing about quantum mechanics is the equations, the mathematics. If you want to understand quantum mechanics, just do the math. All the words that are spun around it don’t mean very much. It’s like playing the violin. If violinists were judged on how they spoke, it wouldn’t make much sense.
E - F
- Die Quantenmechanik ist sehr achtung-gebietend. Aber eine innere Stimme sagt mir, daß das doch nicht der wahre Jakob ist. Die Theorie liefert viel, aber dem Geheimnis des Alten bringt sie uns kaum näher. Jedenfalls bin ich überzeugt, daß der nicht würfelt.
- Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the "old one." I, at any rate, am convinced that He does not throw dice.
- Albert Einstein, Letter to Max Born (4 December 1926); The Born-Einstein Letters (translated by Irene Born) (Walker and Company, New York, 1971) ISBN 0-8027-0326-7.
- What quantum mechanics tells us, I believe, is surprising to say the least. It tells us that the basic components of objects – the particles, electrons, quarks etc. – cannot be thought of as "self-existent". The reality that they, and hence all objects, are components of is merely "empirical reality".
- Bernard d'Espagnat, "Quantum weirdness: What we call 'reality' is just a state of mind", Guardian (20 March 2009)
- However unfamiliar this direct interparticle treatment compared to the electrodynamics of Maxwell and Lorentz, it deals with the same problems, talks about the same charges, considers the interactions of the same current elements, obtains the same capacitances, predicts the same inductances and yields the same physical conclusions. Consequently action-at-a-distance must have a close connection with field theory.
- ...the "paradox" is only a conflict between reality and your feeling of what reality "ought to be."
- Richard Feynman, in The Feynman Lectures on Physics, vol III, p. 18-9 (1965)
- It will be difficult. But the difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, 'But how can it be like that?' which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it. There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics. So do not take the lecture too seriously, feeling that you really have to understand in terms of some model what I am going to describe, but just relax and enjoy it. I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will get 'down the drain', into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.
- Richard Feynman, in The Character of Physical Law (1965)
- We have always had a great deal of difficulty understanding the world view that quantum mechanics represents. At least I do, because I'm an old enough man that I haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it.... You know how it always is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem.
- Richard Feynman, in Simulating Physics with Computers appearing in International Journal of Theoretical Physics (1982) p. 471.
- We choose to examine a phenomenon [Double-slit experiment] which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by "explaining" how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics.
- Richard Feynman, The Feynman Lectures on Physics: Commemorative Issue, Vol. 3 Quantum Mechanics (1989) 1-1, "Quantum Behavior."
- Quantum theory was split up into dialects. Different people describe the same experiences in remarkably different languages. This is confusing even to physicists.
- Many educators, and even politicians, have been firmly convinced that "free will" is not compatible with Newtonian physics, but very much so with quantum theory. They have been convinced also that it is desirable that the citizen should believe in free will, and they have exerted a certain influence in favor of the indeterministic formulation of subatomic physics. What they have in mind is certainly a sociological purpose of science, whatever the technological purposes may be.
- Philipp Frank, Philosophy of Science: The Link Between Science and Philosophy (1957) p. 358.
G - K
- Quantum mechanics, that mysterious, confusing discipline, which none of us really understands but which we know how to use. It works perfectly, as far as we can tell, in describing physical reality, but it is a ‘counter-intuitive discipline’, as social scientists would say. Quantum mechanics is not a theory, but rather a framework, within which we believe any correct theory must fit.
- Murray Gell-Mann, "Questions for the future", Series Wolfson College lectures, 1980. Oxford University Press, Oxford (1981). Also in the collection The Nature of Matter, Wolfson College Lectures 1980. J. H. Mulvey, ed. (Clarendon Press, Oxford, 1981)
- Just a few months after de Broglie's suggestion, Schrödinger took the decisive step... by determining an equation that governs the shape and the evolution of probability waves, or as they became known, wave functions. It was not long before Schrödinger's equation and the probabilistic interpretation were being used to make wonderfully accurate predictions. By 1927, therefore, classical innocence had been lost. Gone were the days of a clockwork universe whose individual constituents were set in motion at some moment in the past and obediently fulfilled their inescapable, uniquely determined destiny. According to quantum mechanics, the universe evolves according to a rigorous and precise mathematical formalism, but this framework determines only the probability that any particular function will happen—not which future actually ensues.
- Brian Greene, The Elegant Universe (1999) Ch. 4 Microscopic Weirdness.
- Quantum mechanics is clearly superior to classical mechanics for the description of microscopic phenomena, and in principle works equally well for macroscopic phenomena. Hence it is at least plausible that the mathematical and logical structure of quantum mechanics better reflect physical reality than do their classical counter parts. If this reasoning is accepted, quantum theory requires various changes in our view of physical reality relative to what was widely accepted before the quantum era, among them the following:
1. Physical objects never possess a completely precise position or momentum.
2. The fundamental dynamical laws of physics are stochastic and not deterministic, so from the present state of the world one cannot infer a unique future (or past) course of events.
3. The principle of unicity does not hold: there is not a unique exhaustive description of a physical system or a physical process. Instead, reality is such that it can be described in various alternative, incompatible ways, using descriptions which cannot be combined or compared.
- Robert B. Griffiths, Consistent Quantum Theory (2002), Ch. 27 : Quantum theory and reality
- Quantum physics, as our new subject is called, answers such questions as: Why do the stars shine? Why do the elements exhibit the order that is so apparent in the periodic table? How do transistors and other microelectronic devices work? Why does copper conduct electricity but glass does not? In fact, scientists and engineers have applied quantum physics in almost every aspect of everyday life, from medical instrumentation to transportation systems to entertainment industries. Indeed, because quantum physics accounts for all of chemistry, including biochemistry, we need to understand it if we are to understand life itself.
Some of the predictions of quantum physics seem strange even to the physicists and philosophers who study its foundations. Still, experiment after experiment has proved the theory correct, and many have exposed even stranger aspects of the theory.The quantum world is an amusement park full of wonderful rides that are guaranteed to shake up the commonsense world view you have developed since childhood.
- Jearl Walker, David Halliday and Robert Resnick, Fundamentals of Physics (10th edition, 2014), Ch. 38 : Photons and Matter Waves
- Einstein was confused, not the quantum theory.
- Stephen Hawking, Lecture at the Amsterdam Symposium on Gravity, Black Holes, and String Theory (June 21, 1997)
- My attitude — I would paraphrase Goering—is that when I hear of Schrödinger's cat, I reach for my gun.
- Stephen Hawking, in a conversation with Timothy Ferris (4 April 1983), as quoted in The Whole Shebang (1998) by Timothy Ferris, p. 345
- Physicists do not believe quantum mechanics because it explains the world, but because it predicts the outcome of experiments with almost miraculous accuracy. Theorists kept predicting new particles and other phenomena, and experiments kept bearing out those predictions.
- John Horgan, The End of Science (1996) p. 70
- Erwin with his psi can do
Calculations quite a few.
But one thing has not been seen:
Just what does psi really mean?
- Erich Hückel, translated by Felix Bloch and quoted in Traditions et tendances nouvelles des études romanes au Danemark (1988) by Ebbe Spang-Hanssen and Michael Herslund, p. 207; also in The Pioneers of NMR and Magnetic Resonance in Medicine : The Story of MRI (1996) by James Mattson and Merrill Simon, p. 278
- It is often stated that of all the theories proposed in this century, the silliest is quantum theory. In fact, some say that the only thing that quantum theory has going for it is that it is unquestionably correct.
- Michio Kaku, in Hyperspace (1995), p. 263
L - N
- In this connection the "classical object" is usually called apparatus, and its interaction with the electron is spoken of as measurement. However, it must be emphasized that we are here not discussing a process of measurement in which the physicist-observer takes part. By measurement, in quantum mechanics, we understand any process of interaction between classical and quantum objects, occurring apart from and independently of any observer. The importance of the concept of measurement in quantum mechanics was elucidated by N. Bohr.
We have defined "apparatus" as a physical object which is governed, with sufficient accuracy, by classical mechanics. Such, for instance, is a body of large enough mass. However, it must not be supposed that apparatus is necessarily macroscopic. Under certain conditions, the part of apparatus may also be taken by an object which is microscopic, since the idea of "with sufficient accuracy" depends on the actual problem proposed. Thus, the motion of an electron in a Wilson chamber is observed by means of the cloudy track which it leaves, and the thickness of this is large compared with atomic dimensions; when the path is determined with such low accuracy, the electron is an entirely classical object.
Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation.
- I would like to describe an attitude toward quantum mechanics which, whether or not it clarifies the interpretational problems that continue to plague the subject, at least sets them in a rather different perspective. This point of view alters somewhat the language used to address these issues—a glossary is provided in Appendix C—and it may offer a less perplexing basis for teaching quantum mechanics or explaining it to nonspecialists. It is based on one fundamental in sight, perhaps best introduced by an analogy.
My complete answer to the late 19th century question "what is electrodynamics trying to tell us" would simply be this:
Fields in empty space have physical reality; the medium that supports them does not.
Having thus removed the mystery from electrodynamics, let me immediately do the same for quantum mechanics:
Correlations have physical reality; that which they correlate does not.
- N. David Mermin, "What is quantum mechanics trying to tell us?", Am. J. Phys. 66, 753 (1998)
- Quantum mechanics is a more general model than classical mechanics, in the same way that Einsteinian relativity is a more general model than Galilean relativity. One picture subsumes the other. Quantum mechanics, pushed to the limit of the large, goes over smoothly into classical mechanics, whereas classical mechanics remains resolutely classical even when pushed to the limit of the small. ...Heisenberg, Schrödinger, Dirac, and the other early quantum mechanicians ...needed to peek at the classical equations in order to set the quantum equations on the right track. They needed... an idea of where the broader theory must eventually lead.
- Michael Munowitz, Knowing: The Nature of Physical Law (2005)
- Quantum mechanics fascinates me. It describes a wide variety of phenomena based on very few assumptions. It starts with a framework so unlike the differential equations of classical physics, yet it contains classical physics within it. It provides quantitative predictions for many physical situations, and these predictions agree with experiments. In short, quantum mechanics is the ultimate basis, today, by which we understand the physical world.
- Jim Napolitano, Preface to the Second Edition of Modern Quantum Mechanics (2011) by J. J. Sakurai
O - P
- In his standoff with Dr. Ramsay of Harvard last fall, Dr. Leggett suggested that his colleagues should consider the merits of the latter theory. "Why should we think of an electron as being in two states at once but not a cat, when the theory is ostensibly the same in both cases?" Dr. Leggett asked.
Dr. Ramsay said that Dr. Leggett had missed the point. How the wave function mutates is not what you calculate. "What you calculate is the prediction of a measurement," he said.
"If it's a cat, I can guarantee you will get that it's alive or dead," Dr. Ramsay said.
David Gross, a recent Nobel winner and director of the Kavli Institute for Theoretical Physics in Santa Barbara, leapt into the free-for-all, saying that 80 years had not been enough time for the new concepts to sink in. "We're just too young. We should wait until 2200 when quantum mechanics is taught in kindergarten."
- Dennis Overbye, "Quantum Trickery: Testing Einstein's Strangest Theory", The New York Times (Dec. 27, 2005)
- I should begin by expressing my general attitude to present-day quantum theory, by which I mean standard non-relativistic quantum mechanics. The theory has, indeed, two powerful bodies of fact in its favour, and only one thing against it. First, in its favour are all the marvellous agreements that the theory has had with every experimental result to date. Second, and to me almost as important, it is a theory of astonishing and profound mathematical beauty. The one thing that can be said against it is that it makes absolutely no sense!
- Roger Penrose, "Gravity and State Vector Reduction", in: "Quantum Concepts in Space and Time" (1986), R. Penrose and C. J. Isham, ed.
- Planck ...devised his quanta theory, according to which the exchange of energy between the matter and the ether—or rather between ordinary matter and the small resonators whose vibrations furnish the light of incandescent matter—can take place only intermittently. A resonator can not gain energy or lose it in a continuous manner. It can not gain a fraction of a quantum; it must acquire a whole quantum or none at all.
- Henri Poincaré, "The Connection Between Ether and Matter," Annual Report of the Board of Regents of the Smithsonian Institution (1912) p.199
Q - Z
- Ask anyone today working on foundational questions in quantum theory and you are likely to hear that there is still no consensus on many of these questions—all the while, of course, everybody seems to be in perfect agreement on how to apply the quantum formalism when it comes to making experimental predictions.
- Maximilian Schlosshauer, Johannes Kofler, Anton Zeilinger, "The interpretation of quantum mechanics: from disagreement to consensus?", Ann. Phys. (Berlin) 525, No. 4, A51–A54 (2013)
- The inner mysteries of quantum mechanics require a willingness to extend one’s mental processes into a strange world of phantom possibilities, endlessly branching into more and more abstruse chains of coupled logical networks, endlessly extending themselves forward and even backwards in time.
- J. C. Ward, Memoirs of a Theoretical Physicist (Optics Journal, Rochester, 2004).
- ... was my first lesson in quantum mechanics, and in a very real sense my last, since the rest is mere technique, which can be learnt from books.
- J. C. Ward, Memoirs of a Theoretical Physicist (Optics Journal, Rochester, 2004).
- Respectable scientists like de Broglie himself accept wave mechanics because it confers coherence and unity upon the experimental findings of contemporary science, and in spite of the astonishing changes it implies in connection with ideas of causality, time, and space, but it is because of these changes that it wins favor with the public. The great popular success of Einstein was the same thing. The public drinks in and swallows eagerly everything that tends to dispossess the intelligence in favor of some technique; it can hardly wait to abdicate from intelligence and reason and from everything that makes man responsible for his destiny.
- Simone Weil, “Wave Mechanics,” On Science, Necessity, and the Love of God, R. Rees, trans. (1968), p. 75
- This theoretical failure to find a plausible alternative to quantum mechanics, even more than the precise experimental verification of linearity, suggests to me that quantum mechanics is the way it is because any small change in quantum mechanics would lead to logical absurdities. If this is true, quantum mechanics may be a permanent part of physics. Indeed, quantum mechanics may survive not merely as an approximation to a deeper truth, in the way that Newton's theory of gravitation survives as an approximation to Einstein's general theory of relativity, but as a precisely valid feature of the final theory.
- Steven Weinberg, Dreams of the Final Theory (1993), Ch. 4. Quantum Mechanics and Its Discontents
- My own conclusion is that today there is no interpretation of quantum mechanics that does not have serious flaws. This view is not universally shared. Indeed, many physicists are satisfied with their own interpretation of quantum mechanics. But different physicists are satisfied with different interpretations. In my view, we ought to take seriously the possibility of finding some more satisfactory other theory, to which quantum mechanics is only a good approximation.
- Steven Weinberg, Lectures on Quantum Mechanics (2nd ed., 2015), Ch. 3 : General Principles of Quantum Mechanics
- Quantum theory does not trouble me at all. It is just the way the world works. What eats me, gets me, drives me, pushes me, is to understand how it got that way. What is the deeper foundation underneath it? Where does it come from? So that we won’t see it as something that is unwelcome by friends that we admire—John Bell and many others—it will be something that will make you say, ‘It couldn’t have been otherwise.’ We haven’t gotten to that stage yet, and until we do, we have not met the challenge that is right there. I continue to say that the quantum is the crack in the armor that covers the secret of existence. To me it’s a marvelous stimulus, hope, and driving force. And yet I am afraid that just the word—‘hope’—is what does not eat, or possess, or drive so many of our colleagues in the field. They’re content to take the theory for granted, rather than to find out where it comes from. But you would hardly feel the drive to find out where from if you don’t feel that the theory is utterly right. I have been brought up from ‘childhood’ to feel that it is utterly right. Here I was, reading that book of Weyl’s at the age of eighteen and just crazy about it.
- For a zeroth slogan about quantum mechanics, I’ve chosen
What’s hard to understand is classical mechanics, not quantum mechanics.
- Peter Woit, "What’s Hard to Understand is Classical Mechanics, Not Quantum Mechanics" (August 11, 2014)
- The world is not as real as we think.… My personal opinion is that the world is even weirder than what quantum physics tells us.
- Anton Zeilinger, quoted in Dennis Overbye, "Quantum Trickery: Testing Einstein's Strangest Theory", The New York Times (Dec. 27, 2005)
- Interpretations of quantum mechanics
- EPR paradox
- Quantum gravity
- Quantum entanglement
- Lectures on Quantum Mechanics (Weinberg)