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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Does a photon instantaneously gain $c$ speed when emitted from an electron?

An excited electron looses energy in the form of radiations. The radiation constitutes photons which move at a speed $c$. But, is the process of conversion of the energy of the electron into the ...
3
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2answers
1k views

Hermitian operator and reality of eigenvalues

Prove or disprove: The eigenvalues of an operator are all real if and only if the operator is hermitian. I know the proof in one way; that is, I know how to prove that if the operator is hermitian, ...
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4answers
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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...
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1answer
1k 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 ...
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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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Which is more fundamental, Fields or Particles?

I hope that I am using appropriate terminology. My confusion about quantum theory (beyond my obvious unfamiliarity with its terminology) is basically twofold: I lack an adequate understanding of ...
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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 ...
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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.
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10answers
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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 ...
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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 ...
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3answers
471 views

What is the difference between $|0\rangle $ and $0$?

What is the difference between $|0\rangle $ and $0$ in the context of $$a_- |0\rangle =0~?$$
12
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2answers
554 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 ...
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1answer
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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 ...
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2answers
703 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 ...
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5answers
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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 ...
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6answers
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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 ...
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4answers
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Heisenberg Uncertainty Principle scientific proof

Heisenberg's uncertainty principle states that: if the x-component of the momentum of a particle is measured with an uncertainty $$\Delta \vec p_x$$ then its x-position cannot, at same time, be ...
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5answers
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What is the connection between Poisson brackets and commutators?

The Poisson bracket is defined as: $$\{f,g\}_{PB} ~:=~ \sum_{i=1}^{N} \left[ \frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} - \frac{\partial f}{\partial p_{i}} \frac{\partial ...
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3answers
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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 ...
11
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4answers
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What exactly is a quantum of light?

I am currently trying to learn some basic quantum mechanics and I am a bit confused. Wikipedia defines a photon as a quantum of light, which it further explains as some kind of a wave-packet. What ...
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2answers
803 views

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 ...
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4answers
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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
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1answer
433 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 ...
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5answers
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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 ...
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4answers
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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 ...
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2answers
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Speed of a particle in quantum mechanics: phase velocity vs. group velocity

Given that one usually defines two different velocities for a wave, these being the phase velocity and the group velocity, I was asking their meaning for the associated particle in quantum mechanics. ...
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584 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 ...
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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?
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6answers
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Linear Algebra for Quantum Physics

A week ago I asked people on this forum what mathematical background was needed for understanding Quantum Physics, and most of you mentioned Linear Algebra, so I decided to conduct a self-study of ...
3
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1answer
554 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, ...
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3answers
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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
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3answers
2k views

Why do we use Hermitian operators in QM?

Position, momentum, energy and other observables yield real-valued measurements. The Hilbert-space formalism accounts for this physical fact by associating observables with Hermitian ('self-adjoint') ...
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4answers
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Collision of two photons

Could someone explain me how will be look like collision of two photons? Will they behave like: Electromagnetic waves, they will interpher with each other and keep they wave nature Particles and ...
5
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1answer
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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 ...
3
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1answer
553 views

Why are eigenfunctions which correspond to discrete/continuous eigenvalue spectra guaranteed to be normalizable/non-normalizable?

These facts are taken for granted in a QM text I read. The purportedly guaranteed non-normalizability of eigenfunctions which correspond to a continuous eigenvalue spectrum is only partly justified by ...
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2answers
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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 ...
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1answer
355 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 ...
3
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2answers
2k views

Group Velocity and Phase Velocity of Matter Wave?

In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?
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5answers
370 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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10answers
3k views

What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
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7answers
2k 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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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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Maximum theoretical data density

Our ability to store data on or in physical media continues to grow, with the maximum amount a data you can store in a given volume increasing exponentially from year to year. Storage devices continue ...
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3answers
3k 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 ...
21
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7answers
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Is (rest) mass quantized?

I learned today in class that photons and light are quantized. I also remember that electric charge is quantized as well. I was thinking about these implications, and I was wondering if (rest) mass ...
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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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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 ...
14
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5answers
891 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 ...
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3answers
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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 ...
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652 views

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 ...