# Tagged Questions

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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### Landau quantization: degeneracy of first level

In some books the degeneracy of one Landau level in a two-dimensional gas of free electrons is calculated in the following way: Note: The electron spin is not considered. Number of states of a free ...
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### Does a wave function describe the motion of electrons or atoms?

I took the course of quantum mechanics a while ago. I do not quite remember all the detail on how to derive the wave function for hydrogen but I still remember the general picture. I think the text ...
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### By what logic does one come to support a certain interpretation of quantum mechanics?

I have been on Wikipedia reading up on the various interpretations of quantum mechanics. I am entering my final semester as an undergraduate and have taken a QM course, so I am familiar with the basic ...
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### Experiment that demonstrates the wave-particle duality of electrons

EDIT : You're about to read the first iteration of my question which is flawed. Please go to the end to see an illustration of what I meant to say. The phenomenon I was talking about is called ...
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### What happens to Pauli's argument (that says that there is no time operator) when applied to $X$ operator for some simple systems?

An argument by Pauli is usually referred to in the literature when it is stated that there cannot be a time operator in quantum mechanics. This argument can be found as a footnote to P63 of W. Pauli, ...
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### Using Dyson formula in Schrodinger picture

From Time-ordering and Dyson series and what I learnt, Dyson formula is used in the situation of interaction picture: $$i\frac{dU_I}{dt} = H_{I}(t)U_I$$ where $H_I(t)$ is interaction Hamiltonian ...
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### Total spin of many photon thermal state [closed]

I need to find the total spin of a large spin 1/2 ensemble in thermal state: I'm trying to find a formula for $\operatorname{Tr}(S^2 \rho)$ where $\rho=\frac{1}{Z}e^{\beta S_z}$ is the thermal state ...
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### Quantum Mechanics: Relate solutions for two dual hamiltonians?

Consider a Hamiltonian in quantum mechanics: $$H_x=-\frac{d^2}{dx^2}+V(x,c)$$ where $x\in\mathbb{R}$ and the potential $V(x,c)$ depends on position $x$ and a continuous parameter $c$. Furthermore, ...
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### Does the Mach-Zender interferometer imply a quantum wave function

If an optical Mach-Zender interferometer that is set up with perfect interference, then at on port no light such be detected, and at the other light will be detected. A common question asked is 'what ...
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### Questions About Quantum Delta Function Potentials [closed]

I didn't think that it would be possible for a wave function to get through the delta function because there is no "leakage" of the wave function through an infinite potential barrier. I can ...
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### Can free particle (eg. unbound electron or proton) have angular momentum other than spin?

I am learning about parity of nucleus and (elementary) particles. For example, proton has a intrinsic parity of $+1$. However, a more general term for parity of proton is $(-1)^l$ where $l$ is orbital ...
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### 4 Photon Entanglement

I know that if you use SPDC (spontaneous parametric down conversion, which is the process in which a photon of a certain energy and frequency is converted into two entangled photons by being passed ...
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### Grover's algorithm - how to capture eventual answer?

I don't fully understand what is the output of algorithm: a. Is it "value Y you search exists in your input", or b. Is it "value Y you search sits in location X of input". And another question: "what ...
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### Quantum ising/heisenberg model, states representation

I am working with a hamiltonian which looks like this (Heisenberg model) I have made a program which computes this hamiltonian using Pauli matrices (spin 1/2). My working space is then the tensor ...
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### How to understand the electric-field operator in quantum optics?

I know the positive field operator $\mathbf{E}^{+}$ is actually an annihilation operator $a$ while the negative field $\mathbf{E}^{-}$ is a creation operator $a^{+}$. I also learned that the ...
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### Emptiness of the atom [duplicate]

If the atom is actually 99.99% empty, why can't we just put our hands or things inside them?
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### Hamiltonian lattice gauge theory with physically observable local degrees of freedom

In my answer at What, in simplest terms, is gauge invariance?, I mentioned that in certain contexts there can be a "gauge theory" with a local symmetry that leave the Lagrangian/Hamiltonian invariant ...
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### STM Limit of Sample Electric Resitivity

What's the highest level of Electric Resistivity that you can measure with a off-the-shelf STM? I believe Normal Samples have around 1*10⁻⁶ Ohm Centimeters.
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### Why doesn't position and momentum commute? [duplicate]

I'm trying to understand the reason for Heisenberg's uncertainty principle which I read is a "fact of nature" rather than an experimental limitation. I found this thread in which the accepted answer ...
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### Stoner-Wohlfarth model for ferromagnetism

I'm studing the Stoner-Wohlfarth model for ferromagnatism on the book Ibach-Luth Solid state physics. During the derivation of the Stoner criterion I found this passage (8.43) not so clear for me: ...
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### Increasing a potential causes increase in energy levels

Suppose a potential $V(x)$, and suppose a bound particle so the allowed energy levels are discrete. Suppose a second potential $\widetilde{V}(x)$ such that $\widetilde{V}(x) \geq V(x)$ for all $x$ (...
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### Does a wave have inertia?

In de Broglie hypothesis, particles have wave nature. The question is does this wave have inertia? If so is it represented in the corresponding wave equation?
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### Intuition for why there are quantum beats in $V$-type but not in $\Lambda$-type atoms

When calculating the emitted intensity of an excited $\Lambda$-type or $V$-type atom with a quantized field (instead of a semiclassical approach with only quantized energy levels) one finds that there ...
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### Projection operators in quantum mechanics

I'm reading a book on quantum mechanics and a topic in there was not well explained. I couldn't find an answer on the web. Say $\psi(x)$ is a position wave function of a one dimensional free particle,...
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### Ehrenfest Theorem and boundary Conditions

In what cases does Ehrenfests Theorem hold? If I look at the wavefunction of electrons in a squared box of length $L$ (with periodic boundary-conditions, $\Psi(0) = \Psi(L)$), then the solution to ...
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### Quantum wells probability

Consider a Brownian particle in a potential landscape with potential well of depth $E_1$ and another potential well of depth $E_2$. In equilibium, what is the likelihood of finding the particle in ...
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### How exactly does string theory make general relativity and quantum mechanics compatible?

Correct me if I'm wrong, but the reason that quantum mechanics and general relativity are incompatible is because the quantum foam at Planck scales renders space-time discontinuous and doesn't allow ...
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### Harmonic oscillator in quantum mechanics

I have brief questions regarding the attachments, which are notes from the book Introduction to Quantum Mechanics by Griffiths which explains the harmonic oscillator case. Any assistance would be ...
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### What actually happens when a photon is absorbed by matter?

In my physics courses so far we've only discussed the before and after of a photon being absorbed by matter. But what actually happens here? How does the light "meld" with the atom that it is incident ...
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### Commutation Relation between Annihilation & Creation Operators and Ascending & Descending Operators

I am currently working on a QD-Cavity system. After the point Heisenberg Equation of motion is obtained from corresponding Hamiltonian of the system, in order to find the expression for bosonic ...
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### Collapse of Wavefunction after space-like Seperated Measurements

Suppose I have a pair of entangled particles, each one goes in a different direction. Now I measure the momentum of one particle and the position of the other at the same time. Because the ...
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### When does a wavefunction get re-created after a collapse? [closed]

Maybe another way of asking this would be, "When is decoherence un-done for a particle?" Example: Consider that we shoot an electron from a gun. Whilst in transit the electron is just a probability ...
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### A good book on spectroscopy

I have found out that there are two kinds of books on spectroscopy: chemistry prospective experimental physics prospective I am looking for a book which contains more or less rigorous theoretical ...
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### Bandgap calculation in MQW structure

In advance I want to apologize for my bad english. My question is about the calculation of a Bandgap of a multiple structure crystal. In this case: AlGaInAs. Lets assume that the distribution is: Al ...
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### Which theoretical models are there between quantum mechanics and cosmology? [closed]

I'm an enthusiast/hobbyist right now and I'm quite curious about the subject of understanding which scales come between the quantum scale (ab initio/first principles) and the macroscopic scale. After ...
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### Feynman path integral interpretation of the Aharonov Bohm effect [closed]

I have recently been reading about the interpretation of the Aharonov-Bohm effect via Feynman's path integral (see viXra:1403.0950). I do not know whether I am missing something, but I do not ...
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### π , σ - atomic transitions with respect to a quantization axis

In the absence of a magnetic field, how does one physically (i.e perhaps in a thought expt) access delta_m = 0 or +-1 transitions since (as I understand it) the choice of quantization axis is ...
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### What happen if adiabatic evolution fails?

Adiabatic theorem states that: A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest ...
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### Why are general wave functions expressed in terms of energy eigenfunctions?

I have read that the eigenfunctions of any hermitian operator can be used as a basis to express any function, but I have only ever really seen the eigenfunctions of the Hamiltonian used. Why is this? ...
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### Why isn't there a Time Operator in Quantum Mechanics? [duplicate]

I was wondering about a scenario where you subject a quantum particle to an intense gravitation field. Why can't we apply a sort of time operator to the particle to see how time changes for the ...
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### Mean energy of free electrons

My textbook states that the mean energy of free electrons within a solid state is given by $$E_{av} = \frac{U}{N} = \frac{\int_0^{k_f}D(k)E(k)dk}{\int_0^{k_f}D(k)dk}$$ where $D(k)$ is the density of ...
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### non-negative energies

Can someone help me with the following question: given the hamiltonian: $H=\frac{1}{2m}(iP-\hbar f(X))(-iP-\hbar f(X))$ where $f(x)$ an analytic real function. prove that the ...
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### How to construct Hermitian(quantum) operator from a physical experiment?

Suppose I want to study a quantum mechanical quantity of a single particle. I have designed an appropriate apparatus, accuracy of which is limited by relevant laws of quantum theory. I have obtained a ...
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### de Broglie's relation derivation

While going through de Broglie's relation in my textbook I was stuck by a derivation: Here $$\ E=mc^2$$ has been applied to photons. That confused me as I thought that mass of photon=0 but a ...
Let's say, we have a composite system $A\otimes B$. We take the basis for $A$ as $|i\rangle,|j\rangle...,$ the basis for $B$ as $|\alpha\rangle,|\beta\rangle....$ Then an entangled state is a state ...