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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Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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110 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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126 views

on quantum steering

I have become interested in quantum steering after listening a talk and tried to read more about it. I think I am more confused now. My understanding is as follows: Sharing a (entangled) state, ...
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78 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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67 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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97 views

Solution of QM tasks by using asymptotics

When we solve QM tasks by solving Schrodinger equation, such as tasks about particle in Morse potential, Poschl-Teller potential and many others, we usually find an approximations (lets call them as ...
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155 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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58 views

Quantum unscrambling

This question is similar to the Phys.SE post Retrodiction in Quantum Mechanics, however, it addresses a different issue: how would you design a machine that can measure a simple quantum system and ...
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120 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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196 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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132 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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61 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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221 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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192 views

The Hamiltonian for clocks?

I am rather a theoretician and looking for a formalism to represent biological clocks by Hermitian operators. The simplest thought model I am looking for is a formal representation of a clock (for ...
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263 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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77 views

What is three-photon interference?

Whilst reading this paper on a quantum processor that performs a type of matrix computation, I came across the concept of 'three-photon interference'. A quick Google search shows that this process is ...
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488 views

projective measurement & POVM

Let us consider the following completely positive map $\mathcal{B}(\mathbb{C}^n)\ni\rho\mapsto L\rho L^\dagger$, where $L\in\mathcal{B}(\mathbb{C}^n)$ is any arbitrary operator (and can have rank ...
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124 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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65 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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146 views

POVM advantage in state discrimination

Suppose we are given the task of discriminating, with minimum error, between a set of states $\{|\psi_1\rangle,|\psi_2\rangle,\ldots,|\psi_N\rangle\}$. In other words, we are given an unknown state ...
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133 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 ...
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437 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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246 views

What is the Landé g factor?

What is the Landé g factor? I know that it gives the relation between magnetic moment and angular moment, but i wanted to know why are those magnitudes related to each other and why is the magnetic ...
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256 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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163 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, ...
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624 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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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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251 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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185 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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29 views

joint probability distribution in QM

The problem of incompatible observables in quantum mechanics is often explained in terms of their (self-adjoint) operators having different sets of eigenstates. This causes their commutator to be ...
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75 views

Where does an LED use energy other than emitting light?

I have a quantum formula describing what kind of photon should be emitted by an LED depending on its voltage. Of course the colour is depending on the material, but every type of LED also needs its ...
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34 views

How does a Bell measurement physically look like?

I do know how Bell states look like. They can be distinguished by doing a Bell measurement. A measurement has 4 possible outcomes (as there are 4 states, which form orthonormal basis). However I have ...
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36 views

Pion decay exercise in Griffiths books

I have questions about pion decay problem. In Griffith "Introduction to Elementary Particles" 1st edition, 1987, question number 10.10 : Analyze $\pi^-$ decay as a scattering process, using the ...
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54 views

How to do time evolution of operators in the Heisenberg Picture while staying in the Heisenberg Picture

Consider the time evolution of an operator in the Heisenberg picture: $$\tag{1}i\hbar \frac{d}{d t} \hat{A}_{H}(t) = \left([ \hat{A}_S(t), \hat H_S (t)] + i\hbar \frac{d}{d t} \hat{A}_S(t) ...
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36 views

Why is the water diamagnetic?

I checked using my permanent magnet that water is diamagnetic. But why is it like that? Does this have any important consequence for life?
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34 views

Geometric measure of entanglement for fermions or bosons?

For a system consisting of multiple components, say, a spin chain consisting of $N\geq 3 $ spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner ...
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32 views

What physical effects cause materialization of a system of particles for a short time?

It is well-known from physics that a photon with enough energy creates a pair of particles: one electron and one positron. This pair of particles can only exist for a short time. This process is ...
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35 views

commutation relations for operators in projected subspaces

I am looking for a consistent re-definition of commutators for certain operators when I work in a projected subspace. Basically, I have a spin defined in terms of 4 Majorana operators $b_{x}$, ...
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61 views

What does it mean “Hawking radiation is in a pure state”?

I'm trying to understand black hole paradox but I'm not sure if I understand what does it mean "Hawking radiation is in a pure state". Does it mean if Hawking radiation is in a mixed state then ...
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36 views

How to calculate the ground states' Berry phases with doubly degeneracy, such as that due to the particle-hole symmetry or time reversal symmetry?

Suppose the ground states of a system are doubly degenerate due to an anti-unitary symmetry $K$, which are $|\psi>$ and $|K\psi>$. If the system is an one-dimensional Fermion system and ...
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25 views

Why does this 'Quantum Pinned' superconductor allow easy repositioning

I'm confused by videos such as this (popular demonstration of 'Quantum Levitation'): https://www.youtube.com/watch?v=Ws6AAhTw7RA So my current understanding of superconductors is that when in the ...
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41 views

In Grover and Shor Algorithms 2 registers of qubits are handled at books, but it's really just one seen as 2?

I found in the literature that we require at least two quantum registers for arithmetics operation. Example: The function $f(x)=x^2$ is then a unitary evolution of the two registers, in this ...
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33 views

How to solve a difficult equation describing large vacuum fluctuations?

Suppose that a Quantum System can be described by the wavefunction $\psi(\vec{x},t)$, but due to the occurence of chaotic noise within the Quantum System, only the "filtered" wavefunction ...
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39 views

Are there resources for simulating and/or theoretically describing solitons?

Recently there are striking new ideas emerging on "lower level" dynamics with respect to quantum mechanics involving fluid mechanics principles, including hints of soliton-like aspects to particle ...
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52 views

Relation between representations/classifications

Generally a quantum system can be characterized in the following way: its states form a representation space for every symmetry group of that system. The representation has to be unitary (or ...
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77 views

What is the symmetry group of this Hamiltonian?

Consider a Hamiltonian $$\hat H=-\partial_x^2-\partial_y^2+(x-y)Q,$$ where $x,y\in[0,a]$ (homogeneous Dirichlet boundary conditions assumed), and $Q$ is some real parameter. When $Q=0$, the ...
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135 views

Majorana zero mode and 1D Ising model

It is known that the one-dimensional (1D) Ising model can be mapped to a free Majorana model using a Jordan-Wigner transformation and its two degenerated ground states are well interpreted by the two ...
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Simplification of matrix-element given the Wigner-Eckardt theorem and Clebsch-Gordon coefficients of a 1,1/2 system

How can I simplify the following matrix-elements $$\left\langle 1,1/2;m_1,m_2\left| S \right| 1,1/2;m_1^{'},m_2^{'} \right\rangle$$ given the Wigner-Eckard theorem $$\left\langle j,m|S|j^{'},m^{'} ...
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63 views

Understanding Tensor Product

Consider the operator $$e^{-i \hat{H} t/\hbar} = e^{-i (\hat{P} \otimes \hat{X}) t/\hbar},$$ where $\hat{X}$ and $\hat{P}$ are position and momentum operator of two different systems. We know that the ...