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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Do generalized Pauli Operators generate SU(n)?

A commonly used generalization of Pauli Operators is the "clock" and "shift" operators summarized here: http://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices Pauli Operators are generators ...
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32 views

Why can't I use Bell's Theorom for faster than light communication?

I read this description of Bell's theorem. I understand he's restating it slightly, so there may be incorrect assumptions there, or I may have some. I think Bell's theorom should lead to FTL ...
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1answer
20 views

wave-particle duality and entanglement

By fundamental definition of a entangled system we can say that if we know the quantum state of one subsystem then we can describe the state of another subsystem. A particle possess wave-particle ...
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1answer
27 views

Infinite potential well with barrier in the middle- symmetric

So I'm having problems with the double infinite potential well given by $$V(x)= \left\{\begin{array}{ll} \infty & -\infty < x < -a-b \\ 0 & -a-b< x < -a \\ V_0 & -a < x ...
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34 views

Uncoupling a coupled oscillator Hamiltonian by change of variables

I'm working on the problem of two entangled harmonic oscillators with Hamiltonian: $$H = \frac{1}{2} [p_1^2 + p_2^2 + k_0(x_1^2 + x_2^2) + k_1(x_1 - x_2)^2].$$ Introducing the variables $x_± = ...
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9 views

Derivation of the Landauer formula for phonons using Nonequilibrium Green's functions

I am currently trying to understand this paper: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.255503 I really like their derivation of the Landauer formula for phonons using ...
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1answer
68 views

Expectation value of Hamiltonian in different pictures of quantum mechanics

We start with the familiar Schrodinger equation: $$ i\hbar \frac{\partial \left|\psi_S\right\rangle}{\partial t} = \hat{H}_S \left|\psi_S\right\rangle $$ As we switch to a different picture than ...
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103 views

When can we assume that the wavefunction is separable

While working out the stationary states of a single particle in a 3d infinite potential box ($V=0$ inside a cuboid of known dimensions, $V=\infty$ everywhere else), I realized I had to assume the ...
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23 views

How to calculate relative branching fractions of the $Z$ boson to specific pairs of “neutral lepton and anti-lepton”?

The PDG is listing values of "$Z$ couplings to neutral leptons" as $$ \begin{eqnarray} g^{\nu_{\ell}} & = & 0.5008 \, \pm \, 0.0008 \\ g^{\nu_{e}} & = & 0.53 \, \pm \, 0.09 \\ ...
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32 views

Mirror symmetry in spin

We just saw parity symmetry and we were told about the experiments to see the non parity symmetry of disintegration, in particular one involving the reaction: $$^{60}Co\longrightarrow^{60}Ni+ e + ...
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21 views

Questions on the degenerate ground states and Lieb-Schultz-Mattis theorem?

For example, let's consider a $N$ spin-1/2 system on a lattice described by the Hamiltonian $H$. My questions are ordered as follows: (1) If $H$ has either global $SU(2)$ spin-rotation symmetry or ...
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16 views

Markovianity vs Ohmic spectral density in Brownian Motion

It is a relationship between the assumption of taking for the spectral density a ohmic behavior ($J(\omega)\sim\omega$) and the fact that the Markovianity of the dynamics arise naturally? Someone has ...
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49 views

Hydrogen Transition Rate from n',l to n',l'

I am trying to solve Problem 9.22 in Griffiths' Intro to Quantum Mechanics (2nd Ed.) that asks to show the spontaneous emission rate for a transition from n,l to n',l' in hydrogen is given by ...
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23 views

Quantum physics particle in a box [on hold]

A problem I've been given states: Without calculation, write down and explain the energy expectation value $\langle H\rangle$ and the uncertainty $σ_H$ for the $ψ_n$ energy eigenstate of the ...
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46 views

How are the Lagrange equation and Feynmann path integral related? [duplicate]

My question is, where could I get some more info on how the Euler-Lagrange equations are related $$ \delta S [y(x)] =0 $$ with the Feynmann path integral formulation $ \int D[y(X)]e^{iS[y(x)]/\hbar} ...
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1answer
90 views

Will all physical quantities unchanged by this transformation?

I am reading an article about Bloch-Floquet state. My questions is in Part II.B and Appendix A of this paper, I will describe them below. The original Schordinger equation we consider is: ...
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74 views

Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle ...
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1answer
40 views

Is there any non-hermitian operator on Hilbert Space with all real eigenvalues?

The property of hermitian is the sufficient condition for eigenvalue being real. Is there any non-hermitian operator on Hilbert Space with all real eigenvalues? If there exist, then can all ...
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1answer
59 views

Why don't we need to normalize wavefunction to find probability distribution?

Consider an unormalized wavefunction of a rotor at $t = 0$, a combination of $n=0$ and $n=2$ states: $$\psi(\phi) = 3 - 2 \cos (2\phi).$$ Find the probability distribution in angle. The ...
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1answer
32 views

Dipole matrix elements through parity argument

I am trying to find the following dipole moment matrix element $(|n,\ell,m\rangle)$. $$e\langle1,0,0|\vec r|2,0,0\rangle$$ I believe that I can say this matrix element is zero because of parity. The ...
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1answer
32 views

Thermodynamic entropy vs. quantum mechanical entropy

Is there a fundamental difference in the definition of entropy when considering the classical thermodynamic picture vs. the quantum mechanical picture, or are they both fundamentally equivalent?
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248 views

Mass or no mass?

Do all forms of energy have a mass? We know by $E=mc^2$ that mass and energy are directly proportional, but there are massless forms of energy such as electro-magnetic waves. I am also told that there ...
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3answers
196 views

What does the Pauli Exclusion Principle say about a superposition of spin states?

Suppose we have an atom. It is commonly said that because of the PEP, two electrons can't be in the ground state unless they have opposite spins, because no two electrons can have the same ...
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1answer
73 views

Calculating the expectation value of a Hamiltonian

I want to calculate the expectation value of a Hamiltonian. I have a wave function that is $$\psi = \frac{1}{\sqrt{5}}(1\phi_1 + 2\phi_2).$$ I want to know if I set this up properly. The ...
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21 views

quantum mechanics. Electromagnetics

In electromagnetics the intensity of a wave is calculated taking the squared of its amplitude. What is the reason why in quantum waves this cannot be applied to calculate it?
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1answer
37 views

Schroedinger equation. Why Potential energy instead of Force?

What is the reason Schroedinger equation is quoted in terms of potential energy instead of force?
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20 views

How do I overlap this two-particle symmetric wavefunction?

Suppose we have a symmetric wavefunction that composed of a two-particle system: $$ \psi_s = \frac{1}{\sqrt 2} \left(|u,A\rangle|v,B\rangle + |v,A\rangle|u,B\rangle\right)$$ where $u_{(x)}$ and ...
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3answers
178 views

Can a wave possess spin?

Since a matter wave is associated with a particle in quantum mechanics, does the wave spins? I mean, can we visualize the spinning of wave or is it possible that the wave spins?
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1answer
38 views

Stern Gerlach Experiment

Since l=0 for a valence electron in 5s state of silver, L=0 and therefore magnetic dipole moment is also 0 which means that the beam should not have deflected at all. So, we introduced the property of ...
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1answer
56 views

Characteristic polynomial of a Matrix

In fact, this problem is more likely to be a math problem. When I read a paper(http://arxiv.org/abs/0707.2875), the author includes the characteristic polynomial for a type of matrix $A_k$ with ...
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18 views

Classical Scattering of Slow Neutrons by a Diatomic Molecule [on hold]

Consider an experiment in which slow neutrons of momentum $\hbar k$ are scattered by a diatomic molecule; suppose that the molecule is aligned along the $y$ axis with one atom at $y=-b$ and the ...
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32 views

Quantization of linear momentum in 'particle in a box' problem [on hold]

I am new in Quantum Mechanics. I am 2nd year UG (Physics Major). I had few conceptions to clear.. I was going through particle in a box problem ...So while deriving that we used the time independent ...
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1answer
25 views

First Order Time Depenent Perturbation theory of particle in magnetic field

So I am dealing with the following hamiltonian, and the following perturbation: $$H=-\mu B_0\sigma_z$$ $$V=\mu B_1(\cos(\omega t)\hat x-\sin(\omega t)\hat y)\cdot{\bf \sigma}$$ I am asked for the ...
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0answers
63 views

Why is $\vert I=1,I_3=1\rangle = -p\bar n$

My book doesn't explain well how to build a doublet of antiparticles that transforms the same way the particle doublet $(p,n)^T$ (proton neutron) does. They claim $$\tag 1 \vert I=1,I_3=1\rangle = ...
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1answer
178 views

How could there be a truly “pure” state?

If the Universe did start from a single point, then wouldn't all particles be fundamentally entangled? How then could there be a truly "pure" state?
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101 views

Quantum entaglement and the arrow of time

I have seen several claims to that quantum mechanics is required to explain the arrow of time which I take to mean the macroscopic irreversibility of physical systems. This is presumably to resolve ...
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40 views

Degeneracy, spherical harmonics

In a 3D oscillator, the energy levels are known to be $(n_x + n_y + n_z + \frac{3}{2})\hbar \omega = (n + \frac{3}{2})\hbar \omega$. Say for $n = 1$, any of the $n$'s can be $1$ and the rest are $0$. ...
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25 views

Transition between two states probability - Perturbation Theory [on hold]

Part (a): Show probability to transit from state i to j is given by: Part (b)i: Use answer in part (a) to find probability Part (b)ii: Use time evolution to find probability Attempt at question: ...
2
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1answer
61 views

How do I simulate this simple quantum circuit in MATLAB

I want to simulate a circuit similar to the one below in MATLAB. If you have a state matrix describing the state of 3 qubits, I understand that you could apply a CNOT matrix tensored with and identity ...
2
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1answer
59 views

Understanding Well Defined States

I am self-studying from a text in QM. Well defined states are mentioned several times. By and large these are consistent and seem to be readily apparent: states of well defined energy are basis kets ...
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1answer
44 views

Converting between (abstract) linear operators and their position representations

Just as we have an abstract state vector $|\psi\rangle$ and its position representation $\psi(\vec{x}) = \langle \vec{x} | \psi \rangle$, how do we transform between a linear operator, say $H$, that ...
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16 views

Off-diagonal terms of the Husimi $Q$ function?

The Husimi $Q$ function of a quantum state $\rho $ is defined as $ Q (\alpha)=\langle \alpha \vert \rho \vert \alpha \rangle $, where $\alpha = (x, p) $ is a phase space coordinate and $\vert \alpha ...
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1answer
92 views

Can “state” be considered a 5th dimension?

I searched for an answer to this question on Google but just found articles that mention either string theory or a 5th dimension in passing (such as Maxwell equations as they relate to Riemann ...
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48 views

Quantum vector space - A complex vector space [duplicate]

Why is vector space of states, a complex vector space? and not a real vector space or perhaps a space based on a new field altogether, which we would have to create specifically for quantum mechanics? ...
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1answer
40 views

A meaningful distinction between determinism and causality

Causality is generally accepted to be a fundamental physical principle. But quantum mechanics is acausal (e.g. there is no 'why' as to the result of a measurement of the position of a particle in an ...
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1answer
40 views

Quantum entanglement on cosmological scales

This may be a foolish question given my limited understanding of QM but here it is. As I understand quantum entanglement basically means that two particles evolve as a single "unit", i.e., are ...
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How can I simulate a model electronic hole?

Suppose I can solve time-dependent Schrödinger equation for several 1D particles (currently 3). I'd like to see, what an electronic hole is and how it behaves — in a series of numerical experiments. ...
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32 views

Ground state of spin in magnetic field

I am trying to solve a time dependent perturbation theory problem, and it involves the Hamiltonian $$H=-\mu B\sigma_z$$ And a perturbation $$V=-\mu B_1\sigma\cdot(\cos(\omega t)\hat x-\sin(\omega ...
11
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2answers
417 views

Why uncertainty principle is not like this?

In Griffiths' QM, he uses two inequalities (here numbered as $(1)$ and $(2)$) to prove the following general uncertainty principle: $$\sigma_A^2 \sigma_B^2\geq\left(\frac{1}{2i}\langle [\hat A ,\hat ...
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0answers
98 views

Degenerate perturbation theory applied to topological degeneracy?

Consider a quantum system described by a gapped Hamiltonian $H_0$ with degenerate ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an ...