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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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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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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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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385 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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222 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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158 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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75 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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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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179 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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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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Estimate of the second shallowest bound state?

Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$ V(x) ~=~0 $$ for $|x| > b $. The potential is assume to support at least two bound states, but might have more, say $n\geq 2$. ...
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Making An Energy Momentum Plot For A Rashba Model (Using Discretization)

I want to make a plot of the Energy versus the Momentum of the Rashba model, using discrete matrices. First Ill show how I did this for the free particle. Subsequently I will show what goes wrong for ...
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33 views

Do coupled angular momentum eigenstates depend on angle between particle positions?

Suppose we have two particles with positions $\vec r_1$ and $\vec r_2$. The corresponding coupled angular momentum eigenstates would be expressed via Clebsch-Gordan coefficients as (according to this ...
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38 views

On the Equivalence of Schrodinger and Heisenberg Descriptions of Quantum Mechanics and Observability

I'm not a physicist, but rather a control (feedback) systems engineer eager to understand more than just a cursory explanation of quantum mechanics. The StackExchange has been an excellent forum for ...
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55 views

Statistics of many body systems in pure states

My understanding of describing a system in thermal equilibrium is that we introduce an ideal thermal reservoir for convenience and then imagine that the system+reservoir samples all states of constant ...
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79 views

Symmetry, gauge, and projective symmetry group (PSG)?

My following questions come from the understanding of the relations between the PSGs for two gauge-equivalent mean-field (MF) Hamiltonians (or MF ansatz). Considering the Schwinger-fermion ...
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35 views

Tunneling from Dirac material into Schrodinger material?

When a Dirac material, like graphene or TI, has a connection with a normal metal which Schrodinger equation govern on their carriers, how could we manipulate the tunneling of electron from Dirac side ...
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24 views

Meaning of Wigner Function In a Single Variable

We know that if we integrate the Wigner function $W(x,p)$ against one of the variables, we get the marginal probability distribution. But how should we interpret say $W(x)$, i.e. its projection into ...
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Para and ortho hydrogen angular momentum values

In Wikipedia, it is said that: Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. ...
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28 views

Local unitary transformation that maximizes overlap

Could anyone point me in the right direction (reference to papers would suffice) regarding the following: Given two quantum states $|\psi\rangle ,|\phi\rangle \in (\mathbb{C}^d)^{\otimes n}$, where ...
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33 views

Detailed Balance for Quantum Master Equations from System Hamiltonians with Degenerate Spectrum

Kossakowski, Andrzej, et al. ("Quantum detailed balance and KMS condition." Communications in Mathematical Physics 57.2 (1977): 97-110) gave a proof that the stationary state of a quantum dynamical ...
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49 views

A quantum mechanical description of a polarizing filter

When a single photon with polarization $\mathbf{a}$ arrives at a linear polarizing filter in the direction $\mathbf{p}$, the photon has a probability of $(\mathbf{a}\cdot\mathbf{p})^2$ to pass through ...
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83 views

“Good” States In Degenerate Perturbation Theory

During the section on Degenerate Perturbation Theory, Griffiths (Introduction to Quantum Mechanics 2ed) starts with a general linear combination of two orthogonal eigenfunctions of $H_0$. He walks ...
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29 views

How does a photon travel through an electron cloud?

We all know that the exact position and exact velocity of an electron in an atom cannot be determined simultaneously, as per the Heisenberg uncertainty principle. We only talk about the probability of ...
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65 views

Problem with derivation of phonons in crystal

In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental ...
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84 views

Question on spin-orbit interaction

When you study the spin-orbit interaction in quantum mechanics, even for a simple hydrogen atom, you find only the electric field in the nucleus reference system, while in the electron reference ...
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85 views

Lack of scale in Schrödinger equation for square-inverse potential

I see that if we set our potential in schrodinger equation to be a inverse-square dependence we don't have a typical unit of length as we have for hydrogen atom. $$-{\hbar^2\over 2m}\nabla^2\psi + ...
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75 views

Integral over a product of two Green's functions

Need some help here on a frequently encountered integral in Green's function formalism. Forgive me since I am a junior student. I have an integral/summation as a product of a retarded and advanced ...
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42 views

Momentum operator of a particle in an electromagnetic field

In quantum mechanics, to all observables correspond some self-adjoint operators. In the absence of an electromagnetic field the momentum operator is clearly $\vec{P}:=\frac{\hbar}{i}\vec{\nabla}$. ...
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62 views

Are universally valid possibilistic theories possible?

This is a spin-off of the following question: Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with knightian freedom the same things in essence? Given that Thomas ...
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64 views

Use of Boltzmann over Maxwell distribution

Why is the Boltzmann distribution used over the Maxwell distribution in many cases such as the derivation of Plancks law of thermal radiation, derivation of Einstein A and B coefficients, Langevin ...
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45 views

About memory effect in E&M when E and B field has dependence in the history of E and B fields

How should one define the memory effect in E&M formally? What is the physical way to visualize the memory effect? How should one understand it intuitively?
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Symmetry and Algebra

I'm trying to get a more concrete idea how symmetry is understood in quantum theories, as broad as possible. Consider a infinitesimal transformation of states in quantum physics of the form: $$ ...
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67 views

Quantum Boltzmann Equation

What is the Quantum Boltzmann equation and what does it describe? I think it describes the propagation of electrons and photons but I am not sure.
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How to prove that the ground state of the Hubbard model is not a Slater determinant?

Of course it is expected. But how to prove it analytically? Slater determinant is mentioned in almost every quantum mechanics textbook. But it is necessary to warn the undergraduate students that not ...
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WKB approximation in two dimensions

Does anybody know how to implement the WKB approximation for the two-dimensional Schrodinger equation with a harmonic oscillator potential: $\frac{1}{2}\Biggl[-\biggl(\frac{\partial^2}{\partial ...
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Does quantum entanglement imply the existence of a non-causal structure connecting space-time together?

In contrast to a "time-like" or "causal" structure connecting space-time together, Does quantum entanglement imply the existence of a "space-like" or "non-causal" structure holding space-time together ...
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Proof involving the fine-structure Hamiltonian of the Hydrogen atom

Given the perturbed Hamiltonian of the Hydrogen atom: $$ ...
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72 views

Relationship between the Black-Scholes model and path integrals

This question was inspired by some interesting comments by Rod Vance on this answer: Minkowski spacetime: Is there a signature (+,+,+,+)? Could you (Rod), or someone else, expand on these comments ...
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109 views

Probability density of Klein-Gordon equation

This may, perhaps, stir some healthy debate; at least I am having some "fun" thinking about it, hopefully I can solicit some outside views too. It is often regarded that the Klein-Gordon equation ...
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48 views

Electron momentum distribution and wavefunction in momentum space

Does there exist any relationship between the electron momentum distribution used in above threshold ionization and the wave function in momentum space? In other words, starting with the wavefunction ...
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33 views

How to load Bose-Einstein Condensates into an optical lattice?

In cold atom experiments, what techniques are used to load Bose-Einstein Condensates into an optical lattice??
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45 views

Continuous Variable Entanglement Measure for the Statistically Mixed State

Can anybody tell me, which is the best entanglement measure for the Continuous Variable Entanglement of a Statistically Mixed State ? I have read that Schmidt decomposition is not valid in this ...
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48 views

superposition versus statistical mixture interpretation

I have an interpretation problem here. It is about the coherent state $$\left|\left.\alpha,\frac{\pi}{2\Omega}\right.\right\rangle = ...
2
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86 views

Coherences in the density matrix

It is said that the off-diagonal elements of density matrix are coherence. When a system interacts with its environment the off-diagonal elements decay and the ...
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49 views

Can someone explain to me the Rocksar-Kivelson Hamiltonian?

The following paper shows the hamiltonian of the 2D quantum dimer gas (page 2) http://www-thphys.physics.ox.ac.uk/people/ClaudioCastelnovo/Talks/050209_MIT.pdf Here are some questions I have. Why ...
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57 views

Literature on the time reversal operator

Time reversal symmetry seems to be a very useful concept and is mentioned in a good number of papers I recently came across. Most of the time people claim that a certain system or Hamiltonian is time ...
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Classical/ Quantum mechanical view of magnetic monopoles

Is there any classical/ quantum mechanical proof for the non-existence of magnetic monopoles? Or is it just lack of experimental evidence that has led us to the conclusion that monopoles do not exist, ...
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What are you studying when you study a Harmonic Oscillator in QM?

This probably is a naive question - so please forgive a self-studier. In the text I am studying, one builds a HO by placing a particle in a potential that increases quadratically from the origin. The ...