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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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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177 views

Helicity operator in Non relativistic limit

Helicity operator in Dirac equation is given by $$H=\frac{\vec{S}\times \vec{P}}{P^{2}}$$ This operator commutes with dirac hamiltonian.We can also define a helicity(with same form) operator in case ...
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121 views

Unitary Operator apply to Entangled vector

I am trying of resolve this exercise: Show that if $|\psi \rangle$ is an entangled state of two Qbits, then the application of a unitary operator of the form $U_1 \otimes U_2$ necessarily generates an ...
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164 views

linear response for a simple harmonic oscillator

Really sorry for this simple question, but I think it will be useful/interesting in general. Consider a quantum simple harmonic oscillator. Add a perturbation $H_I = -\lambda \hat{x}$ Calculate ...
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29 views

Is there anything to prevent paired-up neutrons from a complete overlap

The reason "neutrons don't overlap", as DarenW explained it, has to do with intricate forces at play that take into account the spins, iso-spins and symmetry of the wavefunctions. However, assume I ...
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49 views

How does a photon leave trace of its polarization state in a photon detector but not trace of which direction it came in?

Some quantum erasure experiments involve polarization of photons. In one such experiment with a double slit, a horizontal polarizer is used in front of one slit, and a vertical polarizer is used for ...
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142 views

2D quantum well energy spectrum (analytical vs numerical)

I am trying to understand the energy spectrum difference between the analytical and the approximated solution for a quantum well. The particle is inside a box with domain $\Omega=(0,0)$X$(1,1)$. For ...
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73 views

How large must the Quantum teleportation fidelity have to be in order for it to be useful?

This question relates and stems from my original question. Please read this one and the comments before answering this question. Quantum Teleportation Fidelity I know that for discrete variables ...
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65 views

2-body interaction energy of 3 particles

If only two-body interaction is considered then what's the energy if I put three particles on one site? Assume delta-interaction and interaction strength is proportional to scattering length $a_F$ ...
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137 views

why is the transition $3p^53d^2 \to 3p^63d^1$ (hydrogen atom) forbidden?

What I was thinking is that in 3d subshell (l=2) we have two electrons with $$m_l=-2$$ (spin up and down) and if we move to 3p we will fill the last vacant position - that is $$m_l=1$$ with spin down ...
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75 views

NMR rotating frame

I'm reading about a linearly polarized field (in the context of NMR). The field is given by $$ {\bf H_{lin}}=2H_1({\bf i}cos(\omega_zt)).$$ This can be created by having a pulse field plus its ...
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854 views

How is multiplicity given by 2S+1?

Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}$, $l_1 = 1$ and $s_2 = \frac{1}{2}$, $l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either $+2$, $+1$ ...
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132 views

Consistent histories and Bohm mechanics, many worlds in disguise?

This was posted on here in someone's Phys.SE answer: No, in the many worlds interpretation, every parallel universe is real, but in consistent histories, once you choose your projection operators, ...
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204 views

Matrix manipulation for Dirac matrices

From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix} 0 & \sigma^i \\ -\sigma^i & 0 \end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix} I & 0 \\ 0 & -I ...
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164 views

Polarization photon and Stokes parameters

I have the following situation: About the polarization of the photon, I introduce the basis: Horizontal polarization $|\leftrightarrow>=\binom{1}{0}$ Vertical polarization ...
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108 views

Measurement in Quantum mechanics

I have got a quantum conservative system whose Hamiltonian is $H$. I consider an selfandjoint operator $O$ whose eigenvalues and eigenvectors are: $$O|\psi _{n}\rangle = \lambda _{n}|\psi ...
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87 views

How many ways are there to distribute M excitations of N identical particles among K=3 quantum harmonic oscillators?

I'm trying to numerically calculate a partition function of N non-interacting but identical particles in a 3D SHO. To do this, I'd like to know the degeneracy of $M$ excitations, $N$ indistinguishable ...
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55 views

Length of the orbit (semiclassical orbits)

The Gutzwiller trace is about $$ d(E)=d_{0} (E)+ \sum_{p.o}A_{p}Cos(S(E)\ell_{p}) $$ and $ \ell_{p} $ are the length of the orbit. However my question is, how can one derive the length of the orbit ...
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229 views

Gauge invariance in Laughlin's argument

In Laughlin's gedanken experiment which aims to explain quantization of Hall conductance, one takes the adiabatic derivative of the Hamiltonian with respect to vector potential. Now it seems that it ...
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86 views

Does quantum Zeno effect play role in astrophysics?

For example, do two galaxies situated in proximity reduce the atom decay rate in each other? What happens with decay quanta escaped to infinity? Does the radius of apparent horizon effect the ...
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69 views

Calculating the error by a small change of the potential in Schrodinger equation

In $\mathbb{R}^3$, consider the time-dependent (non-rel) Schrodinger equation with the potential energy $V(\mathbb{x})$. When a small change(e.g., just a small constant $\delta>0$) of V(x) is ...
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145 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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163 views

General question on aligning a quantization axis

I have a general question on how to work with quantization axis. Here is the setup: I am looking at a single two-level atom placed at the origin $(0, 0, 0)$, which is unperturbed in the sense that ...
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76 views

about wavefunction and vector entries

I am beginer of physics and I am studying some very fundamental idea of quantum mechanics by myself. In the introducing book I am reading, there is an example to show a particle diffraced by a slit or ...
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80 views

Asking for references on the variational treatment of spin wave

My idea is the following: We have a system with Hamiltonian $H$, and we know that there is spin wave in this system by some symmetry-breaking arguments. Now we start from the ground state ...
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191 views

Construct the Hamiltonian of electrons on a graphene sheet ( in xy plane)

Graphene is a two-dimensional material formed by carbon atoms in a honeycomb lattice. Because of the symmetry of the honeycomb lattice, the electrons in graphene obey a linear dispersion relation ...
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195 views

Angular momentum confusion

Could somebody please explain what is going on here? We have a system of two indistinguishable spin-1 bosons. We shall adopt the center of mass frame. Let $S$ = total spin $L$ = relative orbital ...
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62 views

Wigner $3j$ symbols

I am trying to determine the expansion that requires using $3j$ symbols; however, I am running into some conceptual snags. First, the expansion produces symbols that have m's that do not agree with ...
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78 views

Correlation function in relaxation in NMR

I am new in this community, I am from a chemistry background. I want to know a detailed solution of a density matrix for a singlet state using the concept of spin lattice relaxation in NMR. I will ...
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44 views

Free Energy and quantum measurement

Free Energy must be expended to reset the state of an measurement apparatus. Is this statement valid in all situations? Is there a Definitive mathematical exposition?
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234 views

Newton's gravitational constant $G$, the reduced Planck constant $\hbar$, the speed of light $c$: the Dream Team of moderators?

The three great constants of Nature are well known: the speed of light $c$ (special relativity), the reduced Planck constant $\hbar$ (quantum mechanics), Newton's ...
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59 views

QND, CSCO, decoherence and Large N limits

While trying to actually understand the difference between QND and CSCO, I went and found the relevant reference doc, Quantum nondemolition measurements: The route from toys to tools. The key example ...
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69 views

Understanding Resonance States in Condensed Matter

What exactly is a resonance state? My understanding so far is that a resonant state appears as a large spike in the DOS of a material due to an adsorbed impurity or vacancy in the lattice and that ...
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37 views

In heterojunction problem, how to align the energy band in presence of bias voltage

For example, SiO$_2$ barrier embeded between Fe magnet and 2-dimensional-electron-gas such as Si. How to align the energy bands of the three materials when an electric field is perpendicular to the ...
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41 views

Random quantum systems with asymmetric Lifshitz tails?

For a quantum mechanical system with a periodic Hamiltonian (Schrödinger operator) $H$, let $N(E)$ be its integrated density of states, i.e. the fraction of eigenvalues in the spectrum $\sigma(H)$ ...
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75 views

four boson quantum system contact interaction

I have to solve this problem. Four bosons moving in 1d harmonic potential (their spin is 0) and interacting through contact interaction defined via delta function. Now, methods that I have to use: a) ...
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474 views

Scattering on delta function potential

Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$. How can one show or explain that ...
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62 views

Efficiently distinguishing mixed quantum states?

Assume we know two different mixed states, p and q, and an efficient (quantum) algorithm for creating such two. Does it follow that there exists a computationally efficient method/measurement for ...
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111 views

What is better than time-dependent perturbation theory if the pointer states aren't energy eigenstates?

Time-dependent perturbation theory works excellently if the interaction is weak and the pointer states are approximately energy eigenstates. However, what if the pointer states are not remotely energy ...
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90 views

usage of partition function in some number of particles in one-dimensional axis

I just learned some introductory quantum meachnics, but not statistical mechanics, so I am curious how partition functions would be used in the following case: Suppose there are three particles in ...
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110 views

Non-Locality and Entanglement

Let’s consider a pair of particles [with their signals] comprising an isolated system. Any change in some property of either particle is due to the signal/s received from the other. Each particle has ...
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99 views

Bohmian Quantum Mechanics diffusion

About one year ago I attended a pretty interesting seminar of Nino Zanghì on the actual state of Bohmian mechanics. Now, during my undergraduate studies, I didn't have the possibility to take a class ...
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287 views

How to find the Green's Functions for time-dependent inhomogeneous Klein-Gordon equation?

I'm trying to find the Green's functions for time-dependent inhomogeneous Klein-Gordon equation which is : \begin{align*}‎‎ \left[ -‎ ‎\nabla ‎^2 + ‎‎‎‎\frac{1}{c^2} ‎‎\dfrac{\partial ^2}{\partial ...
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191 views

How important are constrained Hamiltonian dynamics and BRST transformation as a formalism?

I am to study BRST transformations, for which I'm currently trying to understand constrained Hamiltonian dynamics to treat systems with singular Lagrangians. The crude recipe followed is Lagrangian -> ...
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65 views

Unitarity and quantum cosmology

By studying quantum cosmology I was asking myself if the fact that the universe is expanding, so space is expanding and with it I would say that phase space is also expanding, so it's a non-unitary ...
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62 views

spectral eigenvalue staircase and quantum system

in a d-dimensional system of Quantum physics , does the Eigenvalue staircase $ N(E)= \sum_{E_{n}\le E} 1 $ determine ALL the properties of Quantum System ?? for example, let us assume that the ...
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20 views

On Bolte's semiclassical law

i have seen on internet the following, for $ E >> 1 $ the Eigenvalue Staircase can be approximated by $ N(E)= \frac{1}{\pi}argZ(1/2+i \sqrt E ) $ ...
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107 views

Phonon vectors and characteristic length interpretation

Basically I have a set of vectors of unit length, $\{\nu_i\}$, describing the movement of phonons (all orthogonal to each other), $\{\omega_i\}$. Lets say I only have two atoms, $m_1$ and $m_2$. In ...
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75 views

shouldn't we add the oscillating terms into Bohr-Sommerfeld quantization formula

shouldn't be the quantization formula (in one dimension) equal to $ N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq $ ?? where the Oscillating term is just the correction from Gutzwiller trace formula or a ...
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101 views

Identifying fragments when there is a superposition of fragments in quantum Darwinism

In Zurek's theory of quantum Darwinism, information about the pointer states of a system imprint themselves upon fragments of the environment carrying records about the state of the system. ...