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 ...

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What does it mean for a Hamiltonian or system to be gapped or gapless?

I've read some papers recently that talk about gapped Hamiltonians or gapless systems, but what does it mean? Edit: Is an XX spin chain in a magnetic field gapped? Why or why not?
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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): ...
22
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6answers
1k views

Simple example showing why measurement & interaction are different

Does someone know of a clear (pedagogical) example where one can really see(with the math) where interaction and measurement are not synonymous in quantum mechanics? I know that every measurement ...
21
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3answers
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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 ...
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7answers
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Are these two quantum systems distinguishable?

Suppose Stanford Research Systems starts selling a two-level atom factory. Your grad student pushes a button, and bang, he gets a two level atom. Half the time the atom is produced in the ground ...
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3answers
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Why can't quantum teleportation be used to transport information?

Kaku Michio says in an interview that we've teleported photons, cesium atoms and beryllium atoms. Having watched a lot of Kaku as well as way too many astrophysics documentaries in general, I know ...
16
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5answers
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What combinations of realism, non-locality, and contextuality are ruled out in quantum theory?

Bell's inequality theorem, along with experimental evidence, shows that we cannot have both realism and locality. While I don't fully understand it, Leggett's inequality takes this a step further and ...
19
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10answers
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Does the Pauli exclusion principle instantaneously affect distant electrons?

According to Brian Cox in his A night with the Stars lecture$^1$, the Pauli exclusion principle means that no electron in the universe can have the same energy state as any other electron in the ...
7
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1answer
703 views

Normalizing Propagators (Path Integrals)

In the context of quantum mechanics via path integrals the normalization of the propagator as $$\left | \int d x K(x,t;x_0,t_0) \right |^2 ~=~ 1$$ is incorrect. But why? It gives the correct ...
5
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5answers
2k views

Commutator algebra in exponents

Considering $X$ and $Y$ such that $[X,Y]=\lambda$, which is complex, and $\mu$ is another complex number, prove: $$e^{\mu(X+Y)}=e^{\mu X} e^{\mu Y} e^{-\mu^2\lambda/2}$$ My attempt (so far) is: ...
12
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2answers
1k views

Does every hermitian operator represent a measurable quantity?

In Quantum mechanics, observables are represented by hermitian operator. But does every hermitian operator represent a observable? If not , how do we know that whether a hermitian operator represent ...
10
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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
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3answers
1k views

Study Quantum Physics

I'm an aspiring physicist who wants to self study some Quantum Physics. My thirst for knowledge is unquenchable and I can not wait 2 more years until I get my first quantum physics class in ...
7
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1answer
538 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 ...
4
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1answer
887 views

What physical significance has the Heisenberg Group?

I read that the canonical commutation relation between momentum and position can be seen as the Lie Algebra of the Heisenberg group. While I get why the commutation relations of momentum and momentum, ...
10
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2answers
840 views

Trouble understanding the Bohr model of the atom

In this article it says: The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. ...
9
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3answers
2k 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 ...
8
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1answer
2k views

Why does photon have only two possible eigenvalues of helicity?

Photon is a spin-1 particle. Were it massive, its spin projected along some direction would be either 1, -1, or 0. But photons can only be in an eigenstate of $S_z$ with eigenvalue $\pm 1$ (z as the ...
3
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3answers
1k views

Can we have discontinuous wavefunctions in the Infinite Square well?

The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
7
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2answers
4k views

Conservation of Energy in a magnet

When a permanent magnet attracts some object, lets say a steel ball, energy is converted into for instance kinetic energy and heat when attraction happens, and they eventually collide. Does this imply ...
22
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7answers
3k views

Quantum mechanics on a manifold

In quantum mechanics the state of a free particle in three dimensional space is $L^2(\mathbb R^3)$, more accurately the projective space of that Hilbert space. Here I am ignoring internal degrees of ...
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3answers
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A “Hermitian” operator with imaginary eigenvalues

Let $${\bf H}=\hat{x}^3\hat{p}+\hat{p}\hat{x}^3$$ where $\hat{p}=-id/dx$. Clearly ${\bf H}^{\dagger}={\bf H}$, because ${\bf H}={\bf T} + {\bf T}^{\dagger}$, where ${\bf T}=\hat{x}^3\hat{p}$. In this ...
28
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6answers
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Canonical everyday-life example of a technology that could not work without humans mastering QM in analogy to the application of GR in GPS?

The GPS is a very handy example in explaining to a broad audience why it is useful for humanity to know the laws of general relativity. It nicely bridges the abstract theory with daily life ...
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3answers
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Noether theorem, gauge symmetry and conservation of charge

I'm trying to understand Noether's theorem, and it's application to gauge symmetry. Below what I've done so far. First, the global gauge symmetry. I'm starting with the Lagragian ...
17
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4answers
763 views

Separability axiom really necessary?

I know other people asked the same question time before, but I read a few posts and I didn't find a satisfactory answer to the question, probably because it is a foundational problem of quantum ...
21
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6answers
938 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 ...
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3answers
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How does one determine ladder operators systematically?

In textbooks, the ladder operators are always defined," and shown to 'raise' the state of a system, but they are never actually derived. Does one find them simply by trial and error? Or is there a ...
4
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2answers
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Classical Limit of the Feynman Path Integral

I understand that in the limit that h_bar goes to zero, the Feynman path integral is dominated by the classical path, and then using the stationary phase approximation we can derive an approximation ...
13
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3answers
730 views

Why does spin have a discrete spectrum?

Why is it that unlike other quantum properties such as momentum and velocity, which usually are given through (probabilistic) continuous values, spin has a (probabilistic) discrete spectrum?
8
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1answer
867 views

Operator Ordering Ambiguities

I have been told that $$[\hat x^2,\hat p^2]=2i\hbar (\hat x\hat p+\hat p\hat x)$$ illustrates operator ordering ambiguity. What does that mean? I tried googling but to no avail.
16
votes
2answers
938 views

What Hermitian operators can be observables?

We can construct a Hermitian operator $O$ in the following general way: find a complete set of projectors $P_\lambda$ which commute, assign to each projector a unique real number $\lambda\in\mathbb ...
9
votes
4answers
2k views

What does a de Broglie wave look like?

What does a de Broglie wave look like? Are de Broglie waves transverse or longitudinal? Can they be polarized? What about the de Broglie wave of a ground state neutral spin-zero Helium 4 atom? ...
8
votes
2answers
6k views

How does quantum trapping with diamagnets work?

I just saw this demonstration by someone from a Tel Aviv University lab. What they achieved there is mind blowing. I myself own a levitron that uses the Hall effect to levitate a magnet, the problem ...
7
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4answers
2k views

Can Planck's constant be derived from Maxwell's equations?

Can mathematics (including statistics, dynamical systems,...) combined with classical electromagnetism (using only the constants appearing in chargefree Maxwell equations) be used to derive the Planck ...
10
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6answers
2k views

Will Determinism be ever possible?

What are the main problems that we need to solve to prove Laplace's determinism correct and overcome the Uncertainty principle?
6
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1answer
594 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 ...
19
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1answer
1k views

Is the Uncertainty Principle valid for information about the past?

My layman understanding of the Uncertainty Principle is that you can't determine the both the position and momentum of a particle at the same point in time, because measuring one variable changes the ...
16
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7answers
2k views

Does Quantum Mechanics assume space and time are continuous?

I was confused when I was listening to a Quantum Mechanics lecture online. Are space and time assumed to be continuous or discrete in Quantum Mechanics? I can see the question is vague, but this is ...
9
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1answer
851 views

exponential potential $ \exp(|x|) $

For $a$ being positive what are the quantisation conditions for an exponential potential? $$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$ with boundary conditions $$ y(0)=0=y(\infty) $$ I ...
6
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4answers
751 views

Is uncertainty principle a technical difficulty in measurement? [duplicate]

Is the uncertainty principle a technical difficulty in measurement or is it an intrinsic concept in quantum mechanics irrelevant of any measurement? Everyone knows the thought experiment of measuring ...
5
votes
4answers
3k views

What does it mean (how is it visualized) for a particle to act as a wave?

I have no background in physics. This isn't for homework, just for interest. In quantum physics, it's described that a particle can act as both a particle and a wave. Quoted from HowStuffWorks ...
4
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1answer
204 views

Two-Person Problem

The following is a thought experiment I've been stuck on. (No, this isn't homework. I made it up.) Here it is: Two-Person Problem Let's say we have a superposed particle going through a tube. ...
3
votes
2answers
1k views

EPR-type experiments and faster-than-light communication using interference effects as signaling mechanism

I understand that faster-than-light communication is impossible when making single measurements, because the outcome of each measurement is random. However, shouldn't measurement on one side collapse ...
17
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4answers
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How to tackle 'dot' product for spin matrices

I read a textbook today on quantum mechanics regarding the Pauli spin matrices for two particles, it gives the Hamiltonian as $$ H = \alpha[\sigma_z^1 + \sigma_z^2] + ...
6
votes
1answer
898 views

Bohr-Sommerfeld quantization from the WKB approximation

How can one prove the Bohr-Sommerfeld quantization formula $$ \oint p~dq ~=~2\pi n \hbar $$ from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? With $S$ the ...
3
votes
1answer
144 views

Why is orbital angular momentum quantized according to $I= \hbar \sqrt{\ell(\ell+1)}$?

I simply have no idea how this result is found $$I=\hbar \sqrt{\ell(\ell+1)}.$$ The result seems to just be dumped in textbooks rather than explained. I can get the result that $I_z=\hbar m_j$. ...
5
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5answers
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How can the nucleus of an atom be in an excited state?

An example of the nucleus of an atom being in an excited state is the Hoyle State, which was a theory devised by the Astronomer Fred Hoyle to help describe the vast quantities of carbon-12 present in ...
2
votes
5answers
439 views

Wave/particle duality

Apologies if this has been asked before (I did check and I believe it wasn't). I have a question about the particle/wave duality of photons (or other particles). Depending on what and how we measure ...
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2answers
2k views

Prove $[A,B^n] = nB^{n-1}[A,B]$

I am trying to show that $[A,B^n] = nB^{n-1}[A,B]$ where A and B are two Hermitian operators that commute with their commutator. However, I am running into a little problem and would like a hint of ...
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1answer
368 views

confusion on quantum field theory [closed]

Having read Art Hobsons paper on Quantum field theory, he states " the field collapses into a field of atomic size" This seems to be stating that each field quanta is a different quantum field? Like 2 ...