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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32 views

Normalisation of angular wave function: particle in a circular box

For a particle in a circular box (with radius $R$) with zero potential inside the circle and infinitely high potential outside of the circle, the Schrödinger equation in polar coordinates is: $$-\...
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1answer
30 views

What's the case when positron electron annihilation gives a photon with least frequency

What is the case when a positron electron annihilation gives two photons and one of the photons has as small frequency as possible? I guess it is when the electron and positron are at rest before they ...
0
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1answer
78 views

Why Doesn't Einstein Get More Credit for Being the Father of Quantum Theory? [closed]

I'm not simply referring to the notion that Einstein treated the discrete emission and transference of energy (and matter) as "real" physical phenomena, but rather his major continuous role in the ...
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0answers
31 views

Did de Broglie deduce E=pc? [on hold]

IIUC, $E=mc^2$ follows from $E=pc$ if $p=mc$ and $pc=hf$ is the same equation as the deBroglie wavelenth. Is it safe to say that $E=pc$ is an equation by de Broglie or is that equation some other ...
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0answers
22 views

Existence of eigenstates in type III staggered semiconductor heterojunctions?

Two semiconductors are aligned in the type III staggered fashion and sandwiched in between infinite potentials. Can there be an eigenstate across the valence band of one material and the conduction ...
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0answers
17 views

Is the bandgap energy at the same level quantasized as other orbits of electrons?

Usually to excite an electron to an 'higher orbit' there has to be an exact quantity of energy of a photon. I don't know hów exact this quantity of photonenergy has to be, but is there a difference ...
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0answers
25 views

Can an azimuthally symmetric perturbation lift the 2l+1 degeneracy of angular momentum eigenstates?

Assume the initial Hamiltonian of a spinless, non relativistic particle is $$H_0(r,\theta,\phi)=\frac{{\bf p}^2}{2m}+V_0(r)$$ Such that the eigenstates are angular momentum eigenstates $|n,l,m>$, ...
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1answer
59 views

Density of states from $k$ to $E$

Speaking about Quantum mechanics, considering the "particle in a box" condition as an approximation of the electrons condition in a semiconductor, let the material be represented by a volume $V$ with ...
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0answers
25 views

Mathematica code for self-consistent field loop in Hartree-Fock method

I want to write a Mathematica code for Hartree-Fock treatment of helium (or hydrogen molecule-> namely two electrons systems) , but I don't know how to write a loop for self consistent field procedure....
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0answers
46 views

How to understand the momentum operator in a exponential function? [on hold]

What's the integral expression or matrix expression of the quantum parlance $$U\left( {x - \Delta {x_i}} \right) = \left\langle {x|\exp \left( { - i\Delta {x_i}P} \right)|U} \right\rangle ,$$ where $...
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2answers
60 views

Connection between harmonic potential and particle intepretation

I just finished a quantum mechanics course, but I still have some problems. In the simple harmonics potential well, energy between two adjacent states is always $\hbar\omega$. I read that this can be ...
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0answers
20 views

Is this interpretation of the change in mass of a wave function correct?

I was interested in how a wave function of a single particle in no potential behaves if it was to lose mass. $$\psi = Ce^{ i \sqrt{2mE} x/\hbar}$$ So I took the derivative with respect to the mass, ...
0
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1answer
42 views

Want to measure entanglement of the state [on hold]

Good day, I want to measure the state with concurrence and negativity. I do local unitary transformation with represented by $U\in SU(4)$ (Lie group). After the transformation (rotation of angle) ...
-3
votes
0answers
25 views

3D wave equation of a 3D object [closed]

For an example I have to derive wave equation of a sphere, x^2 +y^2 + z^2 = r^2 and its solution (wave function). Boundary condition can be anything. I like to know about eigenvalue and its use at ...
0
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1answer
51 views

Fermi Dirac distribution and degenerate energy states

In Quantum Mechanics and in semiconductor materials, the number of electrons $N$ in conduction band is usually computed as follows: $$N = \int_{E_c}^{+\infty} g_c(E)f(E)dE$$ where $g_c(E)$ is the ...
1
vote
1answer
83 views

Probability in QM: derivation or interpretation? [duplicate]

It is known that coordinates $C_k\in\mathbb{C}$ of the QM-state vectors $|\psi\rangle$ has an interpretation as probability weights $p_k$ in the whole state through the formula like $|C_k|^2=p_k$. We ...
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0answers
58 views

can mixed quantum states be thought as separable states

A quantum system contained 6 qubits is defined with Hamiltonian $H$, and has an energy spectrum of 36 energy levels. As statistical mechanics point of view, we can ...
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1answer
68 views

What is a Gibbs state?

What is a Gibbs state and what does it differ from a pure state? Say I have a two-level atom and it is described by a Gibbs state $\rho_G = \dfrac{e^{- \dfrac{H}{kT}}}{Z}$. I know $Z$ is a partition ...
2
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0answers
33 views

Bosonization for unequal left/right Fermi velocities

The standard exposition of bosonization/Luttinger liquid theory in textbooks treats the case that left and right channels share the same absolute value of Fermi velocity. Is it possible to relax this ...
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0answers
35 views

What does phase shift represent in a Mach-Zehnder interferometer?

When describing the polarization of a photon, phase refers to the difference in the phases of the polarization components. E.g.: $|\psi\rangle$ = $|L\rangle$ + $i|R\rangle$ can be said to have a ...
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0answers
41 views

Fine Structure and Fine Structure Constant - intuitive relation?

How does the fine structure and fine structure constant relate to each other, intuitively? I've seen $\alpha$ extrapolated as a term in energy calculations for fine structure, but is there a ...
6
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1answer
226 views

Emergence of space from quantum mechanics

Once talking to a visiting professor at my institute, I heard about some simple model that captures the emergence of space coordinates as the eigenvalues of some infinite-dimensional quantum ...
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0answers
29 views

Applicability of wavefunction matching when Hamiltonian (not just potential) varies

A simple tunnelling calculation can be performed for a potential step by calculating the eigenfunctions for the Hamiltonian on either side of the step and matching the wavefunctions (and using ...
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0answers
41 views

Proof of Tridecompositional Uniqueness Theorem (Elby and Bub, 1994)

I'm looking for a proof of the Tridecompositional Uniqueness Theorem (Elby and Bub, 1994). Could someone help me? References: Maximilian Schlosshauer, arXiv:quant-ph/0312059; p.12-13. A. Elby &...
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0answers
63 views

Fundamental coupling constant equation - fine structure, etc [closed]

I'm trying to understand a bit more about the fine structure constant and how it relates to coupling constants in the fundamental forces. It's listed as a coupling constant for fundamental forces - I ...
0
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2answers
74 views

Show that $(x-iy)g(r)$, $z g(r)$ and $(x+iy)g(r)$ are mutually orthogonal [closed]

I want to show that $$\psi_1(x,y,z) = (x-iy)g(r)$$ $$\psi_2(x,y,z) = \sqrt{2}zg(r)$$ $$\psi_3(x,y,z) = -(x+iy)g(r)$$ where $g(r)$ is an arbitrary function of $r = \sqrt{x^2 + y^2 + z^2}$, are ...
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0answers
30 views

Why a positive voltage raises the potential energy of a positive charge and lowers the energy of a negative charge?

I am reading the relation between energy diagram and V, E (electric filed) in a semiconductor from the site (page 47-48). However, I don't quite understand this sentence below. Could anyone explain ...
0
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1answer
39 views

Do energy levels such as $E_c$, $E_v$ have negative values in semiconductors?

In energy band diagram of a semiconductor, do energy levels such as $E_c$, $E_v$ have negative values? Also, why electrons in semiconductor have energy? What is the formula for energy of an ...
1
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1answer
40 views

What is plastic flow?

I read in a book named Introduction To Tribology that when a soft material is in contact with hard material, the soft surface will undergo a plastic flow because it is pressed by the hard asperities ...
2
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0answers
52 views

Efficient Method for Multiplying Angular Momentum Operators

I'm doing a calculation that involves canonical symmetrization of angular momentum. For example: $H_{\text{classical}} = J_x J_y \rightarrow \hat{H}_{\text{quantum}} = \frac{1}{2}(\hat{J_x}\cdot \...
7
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2answers
106 views

Properties of spectrum of a self-adjoint operator on a separable Hilbert space

So, if I understand it correctly, the spectrum of a self-adjoint operator on a Hilbert space $H$ consists of two parts: $ \newcommand{\ket}[1]{\,\lvert{#1}\rangle} \newcommand{\op}[1]{\hat{#1}} $ ...
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0answers
40 views

How to calculate the partial trace [duplicate]

Can anyone help me in explaining how this example below get the reduced density matrix from the density matrix in bipartite system. $$\rho =\frac{1}{4}\begin{pmatrix} 1 & 1 & cos(\frac{\alpha}...
3
votes
2answers
365 views

Double slit experiment; evidence of wavefunction collapse

This video shows the change of a photon's interference pattern in real time of the Young's single and double slit experiment. In this video it is claimed that by adding a detector to view how the ...
1
vote
1answer
55 views

rotation of a state in Bell basis

Suppose I have a state in Bell basis. For example \begin{equation} \rho = \begin{pmatrix} \rho_{11} &0 & 0 & \rho_{14} \\ 0 &\rho_{22} & \rho_{23} & 0 \\ 0 &\rho_{32} &...
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2answers
75 views

The counter-intuitive time scales in atomic physics and nuclear physics

Compare atomic physics and nuclear physics. The interaction in the latter is much stronger than that in the former. However, the typical spontaneous emission time scale in atomic physics is on the ...
0
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1answer
52 views

Reduced Density operator in matrix form

I already read book of Quantum Computation and Quantum Information by Nielsen and Chuang according to reduced density operator and I already understand how to do the reduced density using Dirac ...
0
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1answer
32 views

How does a hydrogen ion gas cool?

Ok I understand that a hydrogen gas of non-ions at a temperature higher than its surroundings exists with many excited electrons. These electrons, either spontaneously or due to collisions, will ...
1
vote
2answers
88 views

How to form the matrix representation of $|O|^3$

I'm interested in getting the matrix representation of the absolute value of an operator. I know the matrix representation of the operator $O$. Now how do I take its absolute value?
1
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0answers
223 views

Intuition behind transforming a Hamiltonian expressed in momentum representation in eigenbasis [closed]

This question is a supplement to a previous question on the same paper. In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve ...
4
votes
2answers
199 views

why does the frequency of a wave remain constant?

They say the frequency of a wave is its fundamental character, thus remain constant throughout its propagation regardless the medium through which it travels. Could anyone explain why frequency of ...
3
votes
1answer
37 views

Reflection and refraction of single photon incident on a glass slab

If a single photon strikes a glass slab of certain thickness, can we make prediction whether it would reflect or refract? On which factor the reflection or refraction of single photon through such a ...
4
votes
2answers
76 views

Is there a relation between spin and the spin group?

In Quantum Mechanics spin appears as one type of angular momentum. Indeed, in Quantum Mechanics one angular momentum on the state space $\mathcal{E}$ is a triplet of observables $\mathbf{J}=(J_1,J_2,...
0
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1answer
66 views

Scientific Confusion [closed]

I'm not a scientist - I have an interest in science, and I like to read books or watch documentaries about science (mostly physics and astronomy). Often I read books by Brian Greene or watch a ...
3
votes
1answer
60 views

What does partial (non-maximum) quantum entanglement mean?

When quantum systems are entangled, they have a "grade of entanglement" which can be quantified e.g. as the entropy of entanglement. There also are states of "maximum entanglement", e.g. the Bell ...
0
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1answer
42 views

Expectation energy for a quantum harmonic oscillator

At 59:14 in this video, the expectation value of the energy of a harmonic oscillator is $$ \langle E \rangle = \int ||\tilde{\Psi}(p)||^2 \frac{p^2}{2m}\ \mathrm dp + \int ||\Psi(x)||^2\frac{m\omega^2}...
2
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2answers
158 views

Quantum Operators: An Identity

I came across the following neat property: For an operator $\hat{A}$ which is a linear combination of creation and annihilation operators, we have: $$ \langle e^{\hat{A}} \rangle = e^{\langle \...
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1answer
40 views

Why does Carbon-12 have zero nuclear spin?

While studying NMR theory, my textbook explained that only nuclei with odd mass numbers are NMR active because they have non-integer spin quantum numbers and nuclei with an even mass number and atomic ...