F-789 (Mecânica Quântica II)
Período diurno, segundo semestre de 2015
Prof. Mário Noboru Tamashiro, ramal: 3521-5339, e-mail: mtamash@ifi.unicamp.br
Departamento de Física Aplicada, sala 7 (andar inferior) do prédio A-5
Participantes da primeira conferência Solvay sobre radiação e os quanta, outono de 1911 (Hotel Metropole, Bruxelas).
Em pé: Robert Goldschmidt, Max Planck, Heinrich Rubens, Arnold Sommerfeld, Frederick Lindemann, Maurice de Broglie, Martin Knudsen, Friedrich Hasenöhrl, Georges Hostelet, Edouard Herzen, James Hopwood Jeans, Ernest Rutherford, Heike Kamerlingh Onnes, Albert Einstein, Paul Langevin;
Sentados: Walther Nernst, Marcel Brillouin, Ernest Solvay, Hendrik Lorentz, Emil Warburg, Jean Baptiste Perrin, Wilhelm Wien, Marie Curie, Henri Poincaré.
Participantes da quinta conferência Solvay sobre elétrons e fótons, outubro de 1927 (Institut International de Physique Solvay, Leopold Park).
Comentários sobre a Mecânica Quântica
Niels Henrik David Bohr:
“For those who are not shocked when they first come across quantum
theory cannot possibly have understood it.”
“Do not presume to tell God what to do.”
“How wonderful that we have met with a paradox. Now we have some hope of making progress.”
“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough.”
“Indeed the finite interaction between object and measuring agencies
conditioned by the very existence of the quantum of action entails... the
necessity of a final renunciation of the classical ideal of causality and a
radical revision of our attitude towards the problem of
physical reality.”
Max Born:
“We have reached the end of our journey into the depth of matter.
We have sought for firm ground and found none. The deeper we penetrate, the
more restless becomes the universe, and the vaguer and cloudier.”
“The question of whether the waves are something ‘real’ or
a function to describe and predict phenomena in a convenient way is a matter of
taste. I personally like to regard a probability wave, even in a 3N-dimensional
space, as a real thing, certainly as more than a tool for mathematical
calculations... Quite generally, how could we rely on probability predictions if
by this notion we do not refer to something real and objective?”
Sir William Henry Bragg:
“God runs electromagnetics on Monday, Wednesday, and Friday by the wave theory, and the devil runs it by quantum theory on Tuesday, Thursday, and Saturday.”
Louis Victor de Broglie:
“Contrary to certain extreme statements of certain idealist
philosophers, I have the deep conviction that a physical reality external
to us exists which is independent of our thoughts and of our imperfect
means of knowing it.”
“However, I was soon forced to abandon this view by the great
difficulties which it presented, and finally accepted the interpretation which
is now orthodox...”
“A general criticism of the usual interpretation of wave mechanics
is that it constitutes a verbosal refusal to provide a real explanation and this is, it seems to me, quite contrary to the principles of sound scientific method.”
Paul Adrien Maurice Dirac:
“I think that there is a moral to this story, namely that it is more important to have beauty in one's equations than to have them fit experiment. If Schrödinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory.”
“There are great difficulties... in connection with the present quantum
mechanics. It is the best that one can do up till now. But, one should not
suppose that it will survive indefinitely into the future. And I think that it
is quite likely that at some future time we may get an improved quantum mechanics in which there will be a return to determinism and which will, therefore, justify the Einstein point of view.”
Freeman John Dyson:
“The student begins by learning the tricks of the trade... Then he begins
to worry because he does not understand what he is doing. This stage often lasts
six months or longer, and it is strenuous and unpleasant. Then quite unexpectedly... the student says to himself: ‘I understand quantum mechanics,’ or rather
he says: ‘I understand now that there isn't anything to be understood...’
For each new generation of students there is less resistance to be broken down before
they fell at home with quantum ideas.”
Sir Arthur Stanley Eddington:
“Schrödinger's wave-mechanics is not a physical theory, but a dodge - and a very good dodge too.”
“Something unknown is doing we don't know what.”
Albert Einstein:
“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.”
“However I cannot seriously believe in it because the theory is incompatible
with the principle that physics is to represent a reality in time and space,
without spookish long-distance effects.”
“Marvelous, what ideas the young people have these days. But I don't believe a word of it.”
“I think that a particle must have a separate
reality independent of the measurements.
That is an electron has spin, location and
so forth even when it is not being measured.
I like to think that the moon is there even
if I am not looking at it.”
Richard Philips Feynman:
“I think I can safely say that nobody understands quantum mechanics.”
“Where did we get that [Schrödinger's equation] from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger.”
“A philosopher once said, ‘It is necessary for the very existence of science that the same conditions always produce the same results.’ Well, they don't!”
“Turning to quantum mechanics, we know immediately that here we get
only the ability, apparently, to predict probabilities. Might I say immediately,
so that you know where I really intend to go, that we always have
had (secret, secret, close the doors!) we always have had a great deal of
difficulty in 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. And
therefore, some of the younger students... 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. It has not yet become obvious to me 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. So that's why I like
to investigate things.”
Werner Karl Heisenberg:
“Can nature possibly be so absurd as it seemed to us in these atomic experiments?”
“The strangest experience of those years was that the paradoxes of
quantum theory did not disappear during this process of clarification; on the
contrary, they became even more marked and more exciting.”
“Quantum theory provides us with a striking illustration of the fact that we can fully understand a connection though we can only speak of it in images and parables.”
“I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.”
“... all the opponents of the Copenhagen interpretation do agree on
one point. It would, in their view, be desirable to return to the reality
concept of classical physics or, to use a more general philosophical term,
to the ontology of materialism. They would prefer to come back to the idea
of an objective real world whose smallest parts exist objectively in the
same sense as stones or trees exist, independently of whether or not we observe them.”
Max Theodor Felix von Laue:
“If that turns out to be true, I'll quit physics.”
Nathaniel David Mermin:
“If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be: Shut up and calculate!”
Wolfgang Ernst Pauli:
“... the conception of a material physical object, as an object whose
nature and constitution is independent of the way it is observed. We have seen
that modern physics, forced by events, had to give up such an abstraction.”
Sir Rudolph Ernst Peierls:
“ ‘Does the world not exist if there is no observer to see it? Does the observer create the world around him?’ My answer is that this is a non-question
because the word ‘existing’ is undefined. In application to everyday
objects we mean by their existing that we can see or touch them, etc., or that we
could do so in suitable circumstances. This is not the meaning implied in the
question. Of course if there is no observer to have any knowledge of a system
there is no quantum mechanical description of it, since this is in terms of an
observer.”
Sir Roger Penrose:
“Quantum mechanics makes absolutely no sense.”
Erwin Rudolf Josef Alexander Schrödinger:
“... de Broglie, so I believe, disliked the probability interpretation
of wave mechanics as much as I did. But very soon and for a long period one had
to given up opposing it and to accept it as an expedient interim solution.”
“If we are going to stick to this damned quantum-jumping, then I regret that I ever had anything to do with quantum theory.”
Ramamurti Shankar:
“Once we have bitten the quantum apple, our loss of innocence is permanent.”
John Archibald Wheeler:
“If you are not completely confused by quantum mechanics,
you do not understand it.”
“Useful as it is under everyday circumstances to say that the world exists ‘out there’ independent of us, that view can no longer be upheld.
There is a strange sense in which this is a
‘participatory universe.’ ”
Informações sobre o curso:
bibliografia, conteúdo, critérios de avaliação e aproveitamento, calendário de provas
Notas de aula:
parte 1,
parte 2,
parte 3
Livros para consulta:
link para arquivos .pdf e .djvu, requer usuário (seu email na DAC, sem @dac.unicamp.br) e senha
Listas de problemas
(manual de soluções do Griffiths disponível na página de livros):
listas 1 a 7
Atenção: atendendo à
solicitação dos alunos, a data do exame/prova substitutiva previsto
para o dia 09/12/15 (próxima 4ª-feira) foi adiado para o
dia 14/12/15 (2ª-feira).
Os seguintes problemas das listas não constarão do exame,
por serem demasiadamente teóricos, periféricos, longos e/ou trabalhosos:
Lista 1: 1,3,6,8,11; lista 2: 4,5,6,7,10; lista 3: 4,8,10,11; lista 4: 2,4,6,9,10; lista 5: 2,4,8; lista 6: 4,5,8; lista 7: 3,9,10.
Provas:
prova 1,
prova 2,
prova 3
“Where did we get that [Schrödinger's equation] from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger.”
“A philosopher once said, ‘It is necessary for the very existence of science that the same conditions always produce the same results.’ Well, they don't!”
“Turning to quantum mechanics, we know immediately that here we get only the ability, apparently, to predict probabilities. Might I say immediately, so that you know where I really intend to go, that we always have had (secret, secret, close the doors!) we always have had a great deal of difficulty in 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. And therefore, some of the younger students... 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. It has not yet become obvious to me 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. So that's why I like to investigate things.”
“The strangest experience of those years was that the paradoxes of quantum theory did not disappear during this process of clarification; on the contrary, they became even more marked and more exciting.”
“Quantum theory provides us with a striking illustration of the fact that we can fully understand a connection though we can only speak of it in images and parables.”
“I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.”
“... all the opponents of the Copenhagen interpretation do agree on one point. It would, in their view, be desirable to return to the reality concept of classical physics or, to use a more general philosophical term, to the ontology of materialism. They would prefer to come back to the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them.”
“If we are going to stick to this damned quantum-jumping, then I regret that I ever had anything to do with quantum theory.”
“Useful as it is under everyday circumstances to say that the world exists ‘out there’ independent of us, that view can no longer be upheld. There is a strange sense in which this is a ‘participatory universe.’ ”
Lista de alunos matriculados: planilha de notas, planilha de faltas
Alguns links/textos interessantes e/ou úteis
Textos didáticos
Notas de aula do curso F-689 (Mecânica Quântica I): arquivo .pdf
Curso on-line de Mecânica Quântica do Prof. Henrique Fleming: link
Curso on-line de Física Moderna II (contém traduções do livro de Griffiths): link
Bernd Thaller, Visual Quantum Mechanics
(livro eletrônico acessível a partir do IFGW):
link
D. F. Styer, Common misconceptions regarding quantum mechanics (artigo em inglês):
arquivo .pdf
C. Singh, Student understanding of quantum mechanics (artigo em inglês):
arquivo .pdf
C. Singh, M. Belloni, W. Christian, Improving students' understanding of quantum mechanics (artigo em inglês):
arquivo .pdf
R. B. Griffiths, T. Norsen, W. A. Harrison, N. Chonacky, P. Shemella, M. Saelim, C. Singh, M. Belloni, W. Christian, Approaches for improving students' understanding of
quantum mechanics (comentários e respostas ao artigo anterior em inglês):
arquivo .pdf
A. Wurm, M. Berg,
Wick calculus (sobre ordenamento normal em segunda quantização,
artigo em inglês):
arquivo .pdf
H.-Y. Fan, C.-H. Lü,
Wick calculus using the technique of integration within an ordered product of operators (sobre ordenamento normal em segunda quantização, artigo em inglês):
arquivo .pdf
T. H. Cooke, J. L. Wood,
An algebraic method for solving central force problems (artigo em inglês):
arquivo .pdf
R. P. Martínez-y-Romero, H. N. Núñez-Yépez, A. L. Salas-Brito,
An su(1,1) algebraic method for the hydrogen atom (método
algébrico para a solução do átomo de hidrogênio,
artigo em inglês):
arquivo .pdf
F. Wilczek,
Quantum mechanics of fractional-spin particles (sobre anyons,
partículas idênticas que interpolam as estatísticas de
bósons e férmions, artigo em inglês):
arquivo .pdf
Epistemologia da mecânica quântica
Episódio em “The Big Bang Theory” com breve descrição do gato de Schrödinger (em inglês, legendado):
video
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por Margreet de Heer, com permissão.
B. d'Espagnat, The Quantum Theory and Reality (artigo em inglês): arquivo .pdfN. D. Mermin, Is the moon there when nobody looks? Reality and the Quantum Theory (artigo em inglês): arquivo .pdf
J. Baggott, Quantum Mechanics and the Nature of Physical Reality (artigo em inglês): arquivo .pdf
J. Clark, Como funciona o suicídio quântico: link
R. Rhodes, Wheeler's Classic Delayed Choice Experiment (sobre a dualidade onda-partícula): link
História da mecânica quântica
Understanding Quantum Physics (série de quatro vídeos do projeto Cassiopeia, em inglês): link
Retrospectiva histórica da mecânica quântica (artigo da Science, em inglês): arquivo .pdf
Uma breve história da mecânica quântica (capítulo 13 do livro de D. R. Bes, em inglês): arquivo .pdf
Biografia de Werner Heisenberg (em inglês): link
Goudsmit sobre a descoberta do spin eletrônico (em inglês): link
Experimentos reais
Experiência de fenda dupla com elétrons (em inglês): link, vídeo
Teletransporte quântico (em inglês): link 1, link 2, link 3
Efeitos quânticos observados experimentalmente em escala macroscópica (artigo em inglês): link
Experiência de fenda simples e fenda dupla com nêutrons (artigo em inglês): arquivo .pdf
Dualidade onda-partícula em experimentos com fulerenos C60 (artigo em inglês): arquivo .pdf
Difração de elétrons por onda eletromagnética estacionária, efeito Kapitza-Dirac (artigo em inglês): arquivo .pdf
Dualidade onda-partícula e emaranhamento quântico em experimentos com fótons (artigo em inglês): arquivo .pdf
Precessão do spin do nêutron (artigo em inglês): arquivo .pdf
Precessão do spin do múon e determinação de seu momento magnético anômalo (artigo em inglês): arquivo .pdf
Oscilações de neutrinos observadas no detector KamLAND (artigo em inglês): arquivo .pdf
Observação de saltos quânticos em um supercondutor (artigo em inglês): arquivo .pdf
Interferência e superposição quântica de objetos massivos nanométricos (artigo em inglês): arquivo .pdf
Visualização de orbitais moleculares usando microscopia de tunelamento com varredura (artigo em inglês): arquivo .pdf
Efeito Hall quântico fracionário (artigo de divulgação em inglês): arquivo .pdf
Visualização de orbitais do átomo de hidrogênio usando microscopia de fotoionização (em inglês): link 1 (comentário), link 2 (artigo)
Alguns exemplos numéricos
Estados ligados em poço de potencial: link
Soluções numéricas da equação de Schrödinger dependente do tempo (reflexão e tunelamento): vídeo 1, vídeo 2, vídeo 3 vídeo 4, vídeo 5, vídeo 6, vídeo 7
Soluções numéricas da equação de Schrödinger dependente do tempo (oscilador harmônico unidimensional): vídeo 1, vídeo 2, vídeo 3
Barreira de potencial (tunelamento e espalhamento): link
Experiência de Stern-Gerlach para spin 1/2: link para aplicativo java
Experiência de Stern-Gerlach com átomos de prata, íons e elétrons: link
Representações gráficas dos harmônicos esféricos: link 1 (requer java), link 2
Visualização das autofunções do átomo de hidrogênio: link
Evolução temporal de 2 férmions em potencial harmônico unidimensional: vídeo 1
Evolução temporal de 2 férmions em poço unidimensional: vídeo 1, vídeo 2
Comparação da evolução temporal de 2 partículas idênticas em poço unidimensional: vídeo 1 (bósons), vídeo 2 (férmions)
Alguns comics relacionados à Mecânica Quântica
Expect Pain: link
Quantum Gradnamics: link 1, link 2, link 3, link 4
“Hides-and-Bored” Principle: link
Heisenberg's Principle of Uncertainty: link
The Creation (Part 3): link
How to Apply the Laws of Physics to Personal Relationships, Vol. 2: link
Quantum Mechanics Explained versus Religion Explained: link
Moments of Clarity: link 1, link 2
Symmetry (Spin-1/2 Playing Card): link
True Things (Quantum Entanglement): link
Complex Conjugate: link
Psi: link
Physics in 10 Easy Steps (Part 2): link
Classical Exclusion: link
Expectation Value: link
A Bunch of Rocks: link
Quantum Geography: link
Quantum Teleportation: link
Dear Physicists: link
Calc-zilla: link
A Simple Puzzle: link
Snow White and the Seven Linear Transformations: link
Eigencats: link
Schrödinger's Cat: link
Schrödinger's Miscalculations: link 1, link 2, link 3, link 4
Schrödinger's Cat: link
The Cheshire Cat gets Weirder: link
Fourier Transform: link
Quantum Observer: link
Commentary: link
Entanglement (Schrödinger's God): link
(Mis)construe: link
Quantum Tunneling: link
Quantum Immortality: link
Quantum Suicide: link
Schrödinger's Comic: link
Quantum Physics: link
Quant... Uhm...: link
Coming to a Universe Near You: link
Many Worlds: link
Entanglement: link
Many Worlds: link
Many World Problem: link
One Too Many Worlds: link
Physics Pick Up Lines: link
2nd Excited State: link
Math Pick Up Lines: link
Yo Mama Jokes (Physics Edition): link
Research Inspiration: link
Rejecta Physica: link
Arguing With a String Theorist: link
Just Imagine the Feynman Diagram: link
There is No Spoon: link
How to Unify Newtonian Physics and Quantum Mechanics: link
Atoms and the Void: link
Confession: link
Talking to God: link
Powers of Two: link
The Higgs Boson: link
Getting Into Not So Hot Water: link
Aragorn: link
The Age of Discovery: link
Destructive Forces: link
Slides: link
Quantum Web Page Superposition: link
Quantum Web Page Entanglement: link