Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the quantum-field-...

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Why do people categorically dismiss some simple quantum models?

Deterministic models. Clarification of the question: The problem with these blogs is that people are inclined to start yelling at each other. (I admit, I got infected and it's difficult not to raise ...
74
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9answers
12k views

Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?

I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance. Am I ...
5
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2answers
1k views

Proving that $i\hbar\frac{\partial}{\partial \mathbf{p}}$ is the operator of $\mathbf{x}$ in momentum space

How can I prove that $i\hbar\frac{\partial}{\partial \mathbf{p}}$ is the operator of $\mathbf{x}$ in momentum space?
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2answers
1k views

Is the uncertainty principle just saying something about what an observer can know or is it a fundamental property of nature?

I ask this question because I have read two different quotes on the uncertainty principle that don't seem to match very well. There are similar questions around here but I would like an explanation ...
10
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1answer
759 views

The choice of measurement basis on one half of an entangled state affects the other half. Can this be used to communicate faster than light?

It is often stated, particularly in popular physics articles and videos, that if one measures a particle A that is entangled with some other particle B, then this measurement will immediately affect ...
4
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3answers
866 views

Uncertainty principle and measurement

I would like to really understand how the uncertainty principle in QM works, from a practical point of view. So this is my narrative of how an experiment goes, and I'm quickly in trouble: we prepare ...
3
votes
2answers
2k views

Is there an observable of time? [duplicate]

In Quantum Mechanics, position is an observable, but time may be not. I think that time is simply a classical parameter associated with the act of measurement, but is there an observable of time? And ...
21
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8answers
4k views

Deterministic quantum mechanics

I came across a very recent paper by Gerard 't Hooft The abstract says: It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a ...
20
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10answers
5k views

Where did Schrödinger solve the radiating problem of Bohr's model?

One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would ...
13
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3answers
4k views

A book on quantum mechanics supported by the high-level mathematics

I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators ...
2
votes
2answers
375 views

Relation between Wave equation of light and photon wave function?

Suppose in our double slit experimental setup with the usual notations $d,D$, we have a beam of light of known frequency $(\nu)$ and wavelength $(\lambda)$ - so we can describe it as $$ξ_0 = A\sin(kx-\...
12
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2answers
3k views

Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?

The standard treatment of the one-dimensional quantum simple harmonic oscillator (SHO) using the raising and lowering operators arrives at the countable basis of eigenstates $\{\vert n \rangle\}_{n = ...
1
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1answer
2k views

Schrödinger function: Separable wave function with even potential function of x

I have done the Problem 2.1 in Griffiths' quantum mechanics, and it seems not making sense to me. What if the wave function isn't symmetric at all? Then obviously the proof doesn't work. The ...
49
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9answers
3k views

Is the uncertainty principle a property of elementary particles or a result of our measurement tools?

In many physics divulgation books I've read, this seems to be a commonly accepted point of view (I'm making this quote up, as I don't remember the exact words, but this should give you an idea): ...
21
votes
2answers
1k views

Local explanation of the Aharonov-Bohm effect in terms of force fields

Here is an interesting paper for the Physics SE community: On the role of potentials in the Aharonov-Bohm effect. Lev Vaidman. Phys. Rev. A 86 no. 4, 040101 (R) (2012). arXiv:1110.6169 [quant-ph]....
22
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6answers
2k views

Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
17
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5answers
1k views

Is there such a thing as “Action at a distance”?

What ever happened to "action at a distance" in entangled quantum states, i.e. the Einstein-Rosen-Podolsky (EPR) paradox? I thought they argued that in principle one could communicate faster than ...
6
votes
3answers
2k views

Learn QM algebraic formulations and interpretations

I have a good undergrad knowledge of quantum mechanics, and I'm interesting in reading up more about interpretation and in particular things related to how QM emerges algebraically from some ...
10
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4answers
3k views

On the nature of the collapse of the wave function

The collapse of the wave function by measurements is one of the most mysterious properties of quantum mechanics. At what scale does the wave function collapse? What are the conditions for a ...
7
votes
1answer
715 views

Time-ordering vs normal-ordering and the two-point function/propagator

I don't understand how to calculate this generalized two-point function or propagator, used in some advanced topics in quantum field theory, a normal ordered product (denoted between $::$) is ...
10
votes
5answers
1k views

Does an electron move from one excitation state to another, or jump?

I'm wondering, when an electron changes state, does it move from one state to another over some (very small) time period? Or does it change from one state to another in no time? If the former, what ...
8
votes
1answer
11k views

Why does the refractive index depend on wavelength? [duplicate]

Why do different wavelength get impeded more or less when in different materials? Moving with the same speed, but a longer physical distance would imply that the fields oscillate less times in the ...
6
votes
3answers
568 views

Why we use $L_2$ Space In QM?

I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space ...
-3
votes
6answers
4k views

Does Quantum Physics really suggests this universe as a computer simulation? [closed]

I was reading about interesting article here which suggests that our universe is a big computer simulation and the proof of it is a Quantum Physics. I know quantum physics tries to provide some ...
10
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2answers
3k views

What causes a black-body radiation curve to be continuous?

The ideal black-body radiation curve (unlike the quantized emission seen from atomic spectra), is continuous over all frequencies. Many objects approximate ideal blackbodies and have radiation curves ...
41
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1answer
4k views

Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view: Anomalies are due to the fact that quantum field ...
27
votes
5answers
4k views

Interpretation of “transition rate” in Fermi's golden rule

This is a question I asked myself a couple of years back, and which a student recently reminded me of. My off-the-cuff answer is wrong, and whilst I can make some hand-waving responses I'd like a ...
16
votes
4answers
2k views

Dimension of Dirac $\gamma$ matrices

While studying the Dirac equation, I came across this enigmatic passage on p. 551 in From Classical to Quantum Mechanics by G. Esposito, G. Marmo, G. Sudarshan regarding the $\gamma$ matrices: $$\...
18
votes
4answers
2k views

What is the physical meaning of a “complete” Hilbert space in QM?

What does the word "complete" means from the physical point of view? I do not understand what it physically means to say that a Hilbert space is a complete vector space.
21
votes
11answers
2k views

Why can't the outcome of a QM measurement be calculated a-priori?

Quantum Mechanics is very successful in determining the overall statistical distribution of many measurements of the same process. On the other hand, it is completely clueless in determining the ...
13
votes
5answers
1k views

What are some useful ways to imagine the concept of spin as it relates to subatomic particles?

The answers in this question: What is spin as it relates to subatomic particles? do not address some particular questions regarding the concept of spin: How are some useful ways to imagine a ...
9
votes
1answer
4k views

Momentum as Generator of Translations

I understand from some studies in mathematics, that the generator of translations is given by the operator $\frac{d}{dx}$. Similarly, I know from quantum mechanics that the momentum operator is $-i\...
13
votes
7answers
3k views

Can a particle be *physically* observed inside a quantum barrier?

I understand that a particle approaching a finite potential barrier with $E < V_0$, there still is a probability of finding the particle on the other side of the barrier due to quantum tunneling. ...
7
votes
1answer
624 views

Hilbert space of a free particle: Countable or Uncountable?

This is obviously a follow on question to the Phys.SE post Hilbert space of harmonic oscillator: Countable vs uncountable? So I thought that the Hilbert space of a bound electron is countable, but ...
8
votes
5answers
4k views

Does entanglement not immediately contradict the theory of special relativity?

Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that does?...
3
votes
4answers
7k views

Mathematical background for Quantum Mechanics [duplicate]

What are some good sources to learn the mathematical background of Quantum Mechanics? I am talking functional analysis, operator theory etc etc...
7
votes
3answers
1k views

Born's Rule, What is the Reason? [duplicate]

As far as I've read online, there isn't a good explanation for the Born Rule. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives ...
6
votes
2answers
698 views

What's wrong with this experiment showing that either FTL communication is possible or complementarity doesn't hold?

The assumptions are: Alice and Bob have perfectly synchronized clocks Alice and Bob have successfully exchanged a pair of entangled photons The idea is simply to have Alice and Bob perform the ...
5
votes
4answers
625 views

Slit screen and wave-particle duality

In a double-slit experiment, interference patterns are shown when light passes through the slits and illuminate the screen. So the question is, if one shoots a single photon, does the screen show ...
20
votes
1answer
576 views

Why exactly do sometimes universal covers, and sometimes central extensions feature in the application of a symmetry group to quantum physics?

There seem to be two different things one must consider when representing a symmetry group in quantum mechanics: The universal cover: For instance, when representing the rotation group $\mathrm{SO}(...
14
votes
5answers
2k views

Consequences of the new theorem in QM?

It seems there is a new theorem that changes the rules of the game in the interpretational debate on QM: http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392 Does this only leave ...
23
votes
3answers
4k views

What's wrong with this derivation that $i\hbar = 0$?

Let $\hat{x} = x$ and $\hat{p} = -i \hbar \frac {\partial} {\partial x}$ be the position and momentum operators, respectively, and $|\psi_p\rangle$ be the eigenfunction of $\hat{p}$ and therefore $$\...
24
votes
6answers
1k views

Is there a theorem that says that QFT reduces to QM in a suitable limit? A theorem similar to Ehrenfest's theorem?

Is there a theorem that says that QFT reduces to QM in a suitable limit? Of course, it should be, as QFT is relativisitc quantum mechanics. But, is there a more manifest one? such as Ehrenfest's ...
6
votes
3answers
14k views

Heisenberg Uncertainty Principle scientific proof

Heisenberg's uncertainty principle states that: $$\sigma(x)\sigma( p_x )\ge \frac {\hbar}{2}.$$ What is the scientific proof of this principle? Operators Uncertainty
16
votes
7answers
2k views

Quantum entanglement vs classical analogy

Consider that we have two balls, one white and one black, and two distant observers A and B with closed eyes. We give the first ball to the observer A and the second ball to the observer B. The ...
14
votes
6answers
3k views

What constitutes an observation/measurement in QM?

Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle. What is the technical definition of an observation/measurement? If I look at a QM system, it ...
11
votes
5answers
19k views

How do electrons jump orbitals?

My question isn't how they receive the energy to jump, but why. When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals (...
9
votes
3answers
3k views

Why the statement “there exist at least one bound state for negative potential” doesn't hold for 3D case?

Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal. However, today I'm doing a homework considering a potential like this:$...
9
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3answers
2k views

What is quantum entanglement?

What is quantum entanglement? Please be pedagogical. Edit: I have updated my background under my profile.
7
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3answers
411 views

References on the non-compositeness of the known elementary particles

What paper(s) or theory(s) describe or prove that the elementary particles that we have determined today cannot be made up of smaller more fundamental particles?