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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Can Pauli exclusion be described locally?

Is it possible, in principle, to define the exclusion principle in a "local" sense, as a property of the tangent space at a point, or a single fiber of a spin bundle? Or does it necessitate a global ...
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227 views

physical intuition behind quasi-bound state formation in feshbach resonance

In Feshbach resonance, by scattering theory formalism it is found that the resonance in cross-section happens when bound state energy of the closed channel is near to the scattering state energy of ...
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60 views

how is feshbach resonance potential term physically produced?

In Feshbach resonance model, a 2*2 potential term with space dependent diagonal and non-diagonal terms is written $\left(\begin{array}{cc} V_{11}(\mathbf{r}) & V_{12}(\mathbf{r})\\ V_{21}(\mathbf{...
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62 views

Alternative ways to take particle tracks photographs in a cloud chamber

I know that the most common type of particle tracks photography is in photographic plates, but i'm using a cloud chamber and I would like to know if there are alternative ways to take photographs of ...
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135 views

What are the assumptions behind “term symbols”?

In multi-electron atoms, the electronic state of the optically active "subshell" is often expressed in "term symbols" notation. I.e. $^{2S+1}L_J$. This presumes that the system of electrons has ...
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300 views

Does natural unit of information and entropy, nat, play special role in the freebit picture?

Please refer this question to understand why I consider the freebit picture important. In short, it is conjectured, that for certain real systems the most complete physical description possible ...
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65 views

Thermalising a sub-system of a larger, interacting system

I'm considering a joint system consisting of a spin-1/2 particle (qubit) and a spin-l particle (reference) coupled via a Hamiltonian $H_0$. At a certain point I want to couple the qubit to a bosonic ...
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126 views

Geometric quantization AND nuclear physics

Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. Geometric quantization is one formalization of the notion ...
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98 views

The nature of the probability distribution for the energy of a photon released via stimulated emission

The vanilla description of stimulated emission (e.g. in the context of an inverted population laser gain medium) says that a photon with some state vector specifying its energy / polarization / ...
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108 views

Approximate energy levels for the following potential

Let's have potential $$ U(r) = -U_{0}e^{-\frac{r}{a}}. $$ I need to find energy levels for particles moving in this field (for an arbitrary values of orbital number $l$). This task isn't exactly ...
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162 views

Partial waves and the velocity expansion of a scattering cross section

I'm confused about the relation between the velocity expansion of a scattering cross section and the angular momentum (partial wave) expansion. For example, for dark matter annihilation, we write $\...
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106 views

The relation between the action of tunneling and the energy

In the semi-classical physics, the probability of the penetration through a barrier is given by $$ p \sim \exp \left( - A_{0} (E) \right), $$ where $A_0$ is the imaginary part of the action and $E$ ...
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168 views

Fock Subspaces and Weight Vectors

This is my first time taking a physics course (I'm a mathematics major), so I'm encountering a lot of new things, which I'm kind of expected to know. In particular, how to work with Bosons. I've got ...
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124 views

Optimality of product input state in quantum channel

Let $\mathcal N^{A_1\rightarrow B_1}_1,..,\mathcal N^{A_1\rightarrow B_1}_k$ be a set of valid quantum evolutions with equal input and output dimensions. And let the effect of a channel on a system $\...
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212 views

Measure energy state of quantum harmonic oscillator

When discussing the quantum mechanical harmonic oscillator we are talking about energy eigenstates. How would one actually measure in which state an harmonic oscillator is in? Could you weigh it and ...
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151 views

What does “quantum theory forbids promiscuous entanglements” mean?

The context is this article about black hole firewalls. The phrase appears on page 3. It appears to be saying that only pairs of particles can be entangled, never multiple particles, and that this ...
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74 views

Infinite quon statistics/Quantum Boltzmann statistics: models and hamiltonians

I learned long ago that there are some exotic classes of statistics. One of them is calleq $q$-on or quon statistics. It is given by $$a_ia^+_j-qa^+_ja_i=\delta_{ij}$$ Infinite statistics (Quantum ...
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287 views

How to set up Schrodinger's equation for an electron (as a charge distribution) under its own electrostatic field

After reading about the hydrogen atom and understanding how Schrodinger's equation explains most part of the atomic spectrum of an hydrogen atom, and also came to know that, it explains most of the ...
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442 views

How is the Geometric Phase measured in the experiment?

I had read some papers that have mentioned the geometric phase (Berry phase) can be used to detect the quantum phase transitions in a quantum many-body system. My question is: How is it measured in ...
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176 views

Laughlin state unique ground state?

In the FQHE, one typically encounters the statement that the $\nu = 1/3$ Laughlin state is a unique exact ground state of a model Hamiltonian where the Haldane pseudopotentials $V_1 \neq 0$ and $V_m = ...
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86 views

Perturbation in Supersymmetric Quantum Mechanics.

To do perturbation analysis of Supersymmetric Quantum Mechanical Hamiltonian, the superpotential is first scaled by a constant $\lambda >> 1$ and then expanded about it's critical point. Finally ...
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142 views

Dyson Series Second Order Term Importance vs. Time

Given a time ordered Dyson series expansion of $$H_I=e^{-\frac{i}{\hbar}\sigma_3t}V_0\sin(\omega t)\sigma_1e^{\frac{i}{\hbar}\sigma_3t}$$ $${\cal T}\exp\left[-\frac{i}{\hbar}\int_0^tH_I(t')dt'\...
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562 views

Hamiltonian of the surface states of a 3D topological insulator

The surface states of a 3D topological insulator (let's say in the (x-y) plane) are sometimes described by the following Hamiltonian : $$H(k)=\hbar v_F (p_x \sigma_x + p_y \sigma_y)$$ or sometimes by :...
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224 views

What is the link between the density matrix and Hestenes' spinors in geometric algebra?

The density matrix (or state matrix) is a generalization of a wave function that is able to describe incoherent superpositions of an N-state system. It is often written as a matrix and observables are ...
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310 views

What is the relationship between consistent histories and path integrals?

As can for example be learned from chapter I.2 of Anthony Zee's Quantum field theory in a nutshell, path integrals can be used to to calculate the amplitude for a system to transition from one state ...
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170 views

Spin polarization of decay products

A relativistic moving particle, e.g. muon $\mu^+$, described by its four-momentum vector $p_\mu$, charge $e$ and with a given spin polarization, ${\bf S}=(S_x,S_y,S_z)$, decays into three particles, e....
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536 views

Is there any simple quantum model by Gerard 't Hooft which can explain the double slit experiment?

This question is directed to Prof. 't Hooft and anybody who is familiar with his papers. It is a reaction to Prof. 't Hooft's question why nobody is excited about his classical models for quantum ...
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64 views

Are there any connections between James–Stein estimator and quantum mechanics?

Very nice statement from wiki: When three or more unrelated parameters are measured, their total MSE can be reduced by using a combined estimator such as the James–Stein estimator; whereas when ...
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994 views

Comparison of different ab-initio codes

One may find on the web a lot of different computational packages to perform "ab-initio" calculations of electron structure of the solids. Usually, the documentation is not quite transparent about the ...
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87 views

Spectrum of a quantum relativistic “distance squared” operator

This question disusses the same concepts as that question (this time in quantum context). Consider a relativistic system in spacetime dimension $D$. Poincare symmetry yields the conserved charges $M$ (...
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309 views

Symmetries of separable potential

For separable potential, say $x^4+y^4$, its symmetry are degenerate. Is that a generic case to every separable potential? I will explain my question: The potential $x^4+y^4$ has $A_1, B_1, A_2, B_2, ...
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200 views

Matter-wave interference from free falling cold atoms

and another exam question, this is about current research: Interference of matter waves has been studied using ultra-cold atoms. The phase of a matter wave for free-falling cold-atoms at time $t$ ...
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2k views

Energy Levels of 3D Isotropic Harmonic Oscillator (Nuclear Shell Model)

One simple way of detailing the very basic structure of the nuclear shell model involves placing the nucleons in a 3D isotropic oscillator. It's easy to show that the energy eigenvalues are $E = \...
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464 views

1D Topological insulator with PT symmetry

Assume I have the Hamiltonian for a 1D topological insulators as: $$H=\sin(P_x) \sigma_x+i \Delta \sigma_{y}+[1-m-\cos(P_x)] \sigma_z $$ where $m$ is the mass term, $P_x$ is the momentum and $\Delta$ ...
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21 views

possibility of interference of electrons during its transition from higher to lower state

They say an electron possesses dual nature (what we call wave-particle duality in order to relate with our everyday world). If it is an electron (definite particle) it too shows wave-like phenomenon ...
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32 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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51 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 \...
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30 views

Distribution of quantum beating among spectral frequencies

Let's imagine that we have 3-level system: ground state $\vert 0 \rangle$ and two excited states $\vert 1 \rangle$, $\vert 2 \rangle$ with similar energies $\hbar \omega _1$ and $\hbar \omega _2$ ...
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57 views

Rigorous way of box normalisation

This is follow up from an answer to my previous question about unitarity in rigged Hilbert space. As it turns out, that there is no idea of unitarity in rigged Hilbert space (hence no meaningful QM ...
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69 views

Free Particle: Time dependence of expectation value of position Paradox

It would be really appreciated if somebody could clarify something for me: I know that stationary states are states of definite energy. But are all states of definite energy also stationary state? ...
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84 views

Some questions about the Kitaev Chain Model

In the paper,'Unpaired Majorana Fermions in Quantum Wires', Kitaev shows that unpaired Majorana Modes can be found at the end of a Quantum Wire for certain conditions. The effective Hamiltonian ...
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38 views

Bound states in two and three dimensional delta potential in non relativistic QM

I would like to find bound state energies in let's say 2D delta function potential. So my eigenvalue equation is: $$(-\frac{1}{2}\Delta - g\delta(r)) \psi = -B \psi$$ and by the means of Fourier ...
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45 views

Wavefunctions “adapted” to the perturbation ? Relation to Faraday effect

I came accross the following statement in a book: If one wants to switch on a magnetic field, one must first choose the appropriate complex unperturbed wave functions (that are "adapted" to the ...
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60 views

Measurement of $L_z$ in a state which includes spin

I'm working through a problem on finding probabilities for measurements performed for quantities associated with one electron in three dimensions with spin. In that case we know that the state space ...
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35 views

Is electron phonon interaction important away from fermi surface?

In weak coupling superconductor, the effective electron phonon interaction can be written as $$ H_{eff}=\frac{1}{2}\sum_{q,k_1,k_2,\sigma_1,\sigma_2} V_{k_1,q}C^{\dagger}_{k_1+q,\sigma_1} C^{\dagger}...
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36 views

Antiunitary operators in the tenfold way

In the classification of free fermion systems in condensed matter, physicists usually divide the systems into ten symmetry classes, first discovered by Altland and Zirnbauer. In their classification, ...
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38 views

Kitaev chaing, time reversel symmetry, particle hole symmetry

I was wondering if the Kitaev chain has time reversal symmetry. I think it probably doesn't because by staking Kitaev chains it is possible to create a so called Chern insulator with propagating ...
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46 views

Second Order Coherence of NOON State

Given the entangled state $\vert NOON \rangle =\frac{1}{\sqrt{2}}(\vert N,0\rangle + \vert 0,N\rangle)$ how can the second order coherence function at time $\tau$ and 0 be calculated? I know that $g^{...
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73 views

Quantization of non-variational systems?

In undergraduate courses the introduction to Hamiltonian mechanics usually starts from a Newtonian view point. One has equations of motions of the form (not sure if it is ok to use covariant notation ...
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68 views

How do I form the four-momentum quantum operator?

I am trying to form the four-momentum quantum operator. These are the steps I have taken so far: The 3-momentum operator is given by $ \hat{p}_{i} = -i\partial_{i} $. This is covariant because it is ...