# Tagged Questions

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### Variable definition in wave function for scattering particle?

For the wave function of a scattered particle when finding the scattering aptitude we have: $$\psi(r)=Ae^{ik_0∙r}+\frac{2\mu}{\hbar^2} ∫G(r-r')V(r')\psi(r')d^3r'$$ I was wondering what the variables ...
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### Can we correctly define momentum operator only by means of position operator and their commutation relation?

In "J.M. Ziman. Electrons and Phonons: The Theory of Transport Phenomena in Solids" the author formally introduces the position (displacement) operator and then defines the momentum operator with the ...
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### Differences between wavefunction, probability and probability density?

I am trying to understand the differences between wavefunction, probability and probability density. There are different definitions on the internet. For example: ...
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### Should Brillouin zone be a continuous object rather than a discrete one in the thermodynamic limit?

For example, just consider a 1D atom chain with $N$ sites and lattice constant $a=2\pi$, under periodic boundary conditions, the crystal momentum reads as $k=\frac{n}{N}\frac{2\pi}{a}=\frac{n}{N}$, ...
692 views

### What is the difference between Feshbach resonance and Fano resonance?

What is the interpretation of "resonance" in Feshbach resonance and Fano resonance? What is the difference of Feshbach resonance and Fano resonance?
232 views

### Definition of energy

What is the definition of energy $E$ given a dispersion relation $\omega=\omega(k)$ where $k=|\vec k|$ and $\omega$ is not necessarily linearly proportional to $k$? What about momentum $\vec p$? This ...
273 views

### Definition of “Quantizing”

Could anyone explain to me what "quantize" means in the following context? Quantize the 1-D harmonic oscillator for which $$H~=~{p^2\over 2m}+{1\over 2} m\omega^2 x^2.$$ I understand that the ...
357 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.
827 views

### The definition of entropy in quantum mechanics

I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc. So I am curious why there are so many different definitions in quantum mechanics while only ...
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### What is the fundamental differences between bound and entangled states

Specifically, are all entangled states considered bound?
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### Observationally indistinguishable quantum states

What does it mean for 2 quantum states to be "observationally indistinguishable"? If I may venture a guess: Does that mean that the set of possible measured values are the same though the ...
814 views

### Entanglement spectrum

What does it mean by the entanglement spectrum of a quantum system? A brief introduction and a few key references would be appreciated.
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### Wave packets v.s. wave trains

Could someone please explain the difference between a wave packet and a wave train? I have rummaged around online but have not been able to find a definitive definition.
461 views

### Common Variables in Quantum Mechanics

I am an eighth grader (please remember this!!!) in need of some guidance in my school project on Quantum Mechanics, Theory, and Logic. I am attempting the create a graph of the Schrödinger Equation ...
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### What are Low-lying energy levels?

I am reading about some canonical transformations of the Hamiltonian (of a system consisting of an electron interacting with an ionic lattice) due to Tomanaga and Lee, Low and Pines. One of the ...
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### In layman's terms, what is a quantum fluctuation?

What causes it and how does it occur? If you do post some mathematics, please explain what each term means too please.
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### Poles, wavefunctions, transmission

Why is it said that $\operatorname{sech}x$ (a transmission amplitude) has a simple pole on the imaginary axis?