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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Point-like nature of particle interaction and wave function non-locality

Let us consider the Hamiltonian for the hydrogen atom $$ ...
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3answers
304 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec ...
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6answers
728 views

What was the need for doing experiments to prove quantum entanglement?

This question comes from someone who is interested in Physics but with no theoretical background. In 1936, EPR presented the thought experiment which later came to be known and quantum entanglement. ...
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8 views

States in valence and conduction band

I often see a Hamiltonian in second quantization written for the valence and conduction band. Now, I was wondering: What are the single-electron states that form the prouct state they act on? So what ...
2
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1answer
113 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation ...
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8 views

Excitation probability given pulse bandwidth and atom linewidth

Consider photon source producing photon pulses with a frequency distribution $f(\omega)$ and a glass tube filled with a gas. The atoms of the gas can be excited by photons with a frequency of ...
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1answer
65 views

Visualisation of electron

first things first, I'm not by any means a physicist nor a student of physics. I study graphic design. Theme of my bachelor thesis is visualisation of physical and mathematical phenomenons, long story ...
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3answers
61 views

Complexity of a physical system

Are there any accepted definitions quantifying the complexity of: a) macroscopic, classical mechanical systems (e.g., a bicycle) b) microscopic systems (ensembles of atoms)? By the way, I'm not ...
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2answers
59 views

Separability of a Hilbert space and its implications for the formalism of QM

In the text I'm using for QM, one of the properties listed for Hilbert space that is a mystery to me is the property that it is separable. Quoted from text (N. Zettili: Quantum Mechanics: Concepts and ...
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1answer
93 views

1D Finite potential well: solutions with $\sinh$ and $\cosh$?

So I am studying the (one dimensional) quantum mechanical finite potential well defined by: $$ V(x) = \cases{0, &|x|>a\cr -V_0, &|x|<a} $$ where $V_0>0$ is a real number. I know ...
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1answer
26 views

Restrictions on Bell-type inequalities

While deriving and proving Bell-type inequalities of the form $|E(a,b)-E(a,b')|+|E(a',b)+E(a',b')|\leq 2$ I know that the conditions on the operators $O_a$ and $O_b$ are that they must be bounded ...
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1answer
62 views

Atom in a box and collapse of the wave-function

Suppose I have an atom trapped in an optically transparent box. I'm assuming the atom is bouncing off of the walls and not bonding, i.e. the center of mass of the atom experiences a square well. Now ...
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2answers
36 views

What role does the Higgs Field play in the universe?

The Higgs field is known as a physical field that covers the entire universe, giving particles their mass. However, that got me thinking if the Higgs field not only gives mass to other particles, but ...
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22 views

Cohen Tannoudji solutions to exercises

Does anyone know where to find the solutions to the exercises of Cohen-Tannoudji's Quantum Mechanics? I am gonna try to do all of them and would like to check.
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2answers
190 views

Is there any physical quantity that does not have uncertainty?

I saw this video and I got a thought: Is there any physical quantity that does not have uncertainty? Basic models are: for lenght for time end energy (so for mass too) and I realized that ...
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1answer
52 views

How to handle the potential $V(x)$ or $V(\phi)$ which is not analytic in QM and QFT

In QM, $$\hat{x}\phi(p)=i\frac{\partial}{\partial p} \phi(p)$$ and when $V(x)$ is an analytic function of $x$, then $$V(\hat{x})\phi(p)=V(i\frac{\partial}{\partial p} )\phi(p)$$ and we can do Taylor ...
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1answer
33 views

Would a semiconductor shined with monochromatic laser light matching its band-gap have a 100% efficiency if all of the light was absorbed & converted?

The idea of transporting power through laser light is an interesting area of research. Conversions of up to 54% have been reported for long distance transmission. I would assume ...
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1answer
39 views

Change in Shannon entropy of a quantum circuit of Hadamard gate and a loop

The following Q&A about reversible computing is available here. It has listed a number of practical scenarios where a reversible circuit can still be dissipating heat. Let's assume that none of ...
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241 views
+250

Horrifying electron gas model

I am given the Hamiltonian, in an exercise called plasmons, and where $\langle, \rangle $ denotes the expectation value. $$ H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_{k_1,k_2,q} V_q ...
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2answers
115 views

How do we know that photon entanglement isn't the result of the photons's states being predetermined?

I know there is evidence that it is not predetermined and I tried reading articles on it but most of them either don't explain the intuition behind the experiment or they speak in a foreign language ...
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1answer
107 views

Deriving a Useful Solution of the Schrödinger Equation [on hold]

How does one derive the fact that $$\psi(t,x) = (\tfrac{2 \pi \hbar t}{m})^{-d/2}\int_{\mathbb{R}^d} e^{im\tfrac{(x-y)^2}{2\hbar t}}\psi_0(y)dy$$ is a solution of the time-dependent Schrödinger ...
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1answer
50 views

Why doesn't the electron lose or absorb energy while remaining in a selected orbit?

Postulate 2: When an electron revolves in any selected orbits, it neither emits nor absorbs energy . The energy of an electron in a particular orbit remains constant. Thus, Bohr, by postulating ...
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2answers
72 views

Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
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4answers
120 views

Virtual particles/quantum tunneling - conservation of energy?

I'm confused as to how the above phenomena can take place since arent they breaking the law of conservation of energy (even, if temporarily)?
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3answers
2k views

What do we see while watching light? Waves or particles?

I'm trying to understand quantum physics. I'm pretty familiar with it but I can't decide what counts as observing to cause particle behave (at least when it's about lights). So the question is what do ...
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0answers
28 views

How to derive a new form of Hamiltonian operator in quantum mechanics using canonical commutation relation?

How does one derive $$\hat{H} = \frac{1}{2}\hat{p}^2m(\hat{q}) - \frac{i}{2}\hat{p}\frac{m'(\hat{q})}{m^2(\hat{q})} + V(\hat{q})$$ from hamiltonian $$\hat{H} = \hat{p}\frac{1}{2m(\hat{q})}\hat{p} + ...
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15 views

Quantum harmonic oscillator doughnut shape

When phase-space trajectory is plotted for classical harmonic oscillator for p(t)=mx0ωcos(ωt +δ0), a circle is obtained. When done same for the quantum harmonic oscillator, why do we get a doughnut ...
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1answer
60 views

Why does the raising and lowering operator not affect total angular momentum?

My notes define: $$ L_{\pm} = L_{x} \pm i L_{y} $$ and states: $$ [L_{z},L_{\pm}] = \pm \hbar L_{\pm} $$ I'm fine with this as it's easy to show the result with some ugly algebra. It then says: ...
3
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1answer
50 views

Does Bell's inequalities also rule out non-computable local hidden variable theories?

I have beenn reading different articles on Bell's assumptions and interpretations, including superdeterminsm. I always end up dizzy when I try tho think about this specific question, so any hints ...
2
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1answer
43 views

Energy in harmonic oscillator [on hold]

The expectation value of the potential energy is exactly half the total according to Griffiths. Is that case always true for quantum harmonic oscillator? Is that the case also for classical harmonic ...
0
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1answer
61 views

How to construct this oracle quantum gate?

I was reading the paper Quantum Computational Complexity in the Presence of Closed Timelike Curves. In this the author mentions that following quantum oracle gate which operates on $n+1$ qubits, can ...
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1answer
42 views

Constructing matrix for spin in Stern-Gerlach experiment for arbitrary angle

This is a conceptual question about a problem in Sakurai. I understand how to solve the problem, but there's something about it that irks me, and it feels like I'm missing something. In the problem, ...
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2answers
57 views

Collapse of the wave function and Heisenberg uncertainty

I have been studying quantum mechanics for a few weeks, in particular wave mechanics, as created by Schrodinger, and his equation. As a high school student, I haven't found an answer to this question ...
2
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4answers
866 views

Which Schrödinger equation is correct?

In the coordinate representation, in 1D, the wave function depends on space and time, $\Psi(x,t)$, accordingly the time dependent Schrödinger equation is $$H\Psi(x,t) = ...
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1answer
38 views

Do entangled particles lose entanglement after polarizing filters?

If two entangled particles are sent through different polarizing filters, do they lose their entanglement after the filters?
4
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3answers
102 views

Why every state evolving infinite time becomes the ground state in QFT?

For any state $|\phi \rangle $ evolving infinite time $$\lim\limits_{t\rightarrow \infty} e^{-iHt}|\phi\rangle=\lim\limits_{t\rightarrow \infty} e^{-iHt}|n\rangle\langle n|\phi\rangle$$ Let ...
0
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1answer
30 views

Eigenvalues of Angular Momentum in Quantum Mechanics

The eigenvalue equation of the $L^2$ operator is given by $$L^2f_l^m = \hbar ^2l(l+1)f_l^m$$ Side: So a determinate state for some observable $Q$ is a state where every measurement of $Q$ returns ...
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0answers
236 views

Why discrepancies in the Schrödinger equation? [duplicate]

Why is there seemingly two definitions of the Schrödinger equation? \begin{equation} i\hbar\frac{\partial}{\partial t}\Psi=\hat H\Psi. \end{equation} And \begin{equation} i\hbar ...
3
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1answer
622 views

Time evolution in quantum mechanics

We know that an operator A in quantum mechanics has time evolution given by Heisenberg equation: $$ \frac{i}{\hbar}[H,A]+\frac{\partial A}{\partial t}=\frac{d A}{d t} $$ Can we derive from this ...
4
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0answers
1k views

Solution for the Finite 2D Potential Well - Rotational Symmetry [closed]

I was searching for the eigensolutions of the two-dimensional Schrödinger equation $$\mathrm{i}\hbar \partial_t \mid \psi \rangle = \frac{\mathbf{p}^2}{2m_e}\mid \psi \rangle + V \mid \psi ...
2
votes
2answers
53 views

Why does Fermi level has a probability density of 1/2 while it may lie in the forbidden region?

I dont understand how there is a continuous probability density function in semiconductors, when there are several regions which are restricted by Energy, i.e. forbidden energies. Well i know that in ...
2
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3answers
603 views

Decoherence and collapse

It is said that the decoherence does not solve the problem of measurement and/or the emergence of classicality, can somebody explain it with simple analogies or in a manner accessible to a ...
2
votes
1answer
98 views

Electron distribution around atom when moving

I do not have much experience on this but if an atom has some electrons around nucleus and the atom itself it is moving at some speed does that affect the distribution of electrons around? I am ...
2
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0answers
24 views

With what fraction photon quanta emission rate is decreased in the expanding universe? [on hold]

Light from edge of the observable universe has travelled 13.8 billion light years so far. And, that edge itself has travelled 32.2-33.2 billion light years (that's why actual radius of observable ...
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0answers
48 views

Quantum Entropy-a minimization problem

I came upon this (not homework) problem of minimizing the following expression ...
1
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3answers
71 views

State vector vs density operator

We formulate quantum mechanics using language of state vectors. One alternative formulation is possible using density operator or density matrix. Why we are doing this alternative approach? Is the ...
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0answers
37 views

Allowed Values of Angular Momentum for a Rotating Mass

I am attempting to calculate all possible values of angular momentum, $L_z$, which can be found by making a measurement on the following system: A small mass, $M$, is attached to the end of a rigid, ...
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46 views

how to prove the following equations? [on hold]

Equations in this image include some confusing steps for me, I tried but no results came out. please if some one can solve it I'll be very thankful.
2
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1answer
47 views

Quasiclassical QM for central fields

Let's have quasiclassical QM for central field $V(r)$. The Schroedinger equation for radial part of wavefunction $R_{nl}$ after substitution $u_{nl} = rR_{nl}$ takes the form $$ u_{nl}{''} + ...
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2answers
77 views

What is the most agreed upon quantum mechanical equation of motion?

On multiple Wikipedia articles, it mentions several quantum mechanical equations of motion, namely those by Schrödinger and Heisenberg. Which one is the most accurate and agreed upon quantum ...