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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Time Dependent perturbation driven at resonance

SO I am looking at driven perturbations, and I came across Fermi's golden rule here. It has a term that goes as: $$P\propto\frac{1}{\omega_{fl}-\omega}$$ Now I am curious how to go about solving this ...
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55 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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32 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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19 views

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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47 views

Heisenberg Uncertainity Principle

If any senior member of the group has access to the book, The Physical Principles of Quantum Theory by W. Heisenberg, then please help me in understanding the first section of chapter 2 where he gives ...
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15 views

Entropy of Reeh-Schlieder correlations

Any state analytic in energy (which includes most physical states since they have bounded energy) contains non-local correlations described by the Reeh-Schlieder theorem in AQFT. It is further shown ...
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74 views

Rewriting $\langle {\bf k} \vert E,l,m \rangle$ as $\langle {\bf k} \vert ~k,l,m \rangle$ Spherical Harmonics

From Sakurai eq. 6.4.21a we have that $$\langle {\bf k} \vert E,l,m \rangle=\frac{\hbar}{\sqrt{M k}}\delta\left(E-\frac{\hbar^2 k^2 }{2M}\right) Y_l^m({\bf\hat k}),$$ where $M$ is the mass of the ...
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27 views

Help with 1D and 2D density of states

I am currently looking at changes in DOS when sampling recipocal space finely. More precisely, I am looking at the expressions $$\rho_\text{1D}(E)\text{d}E = \frac{m}{\pi \hbar} \sum_i ...
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38 views

Physical Meaning of Linear dependence of vectors in quantum mechanics

I have got some questions regarding the mathematical concepts in Quantum Mechanics that I have listed below- 1) What is the physical meaning of linear dependence of vectors in Quantum Mechanics ? 2) ...
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46 views

Mathematical Physics SUSY QM Resource Recommendation

I want to study SUSY QM. I found some excellent physically motivated articles on Arxiv. Despite, I am especially interested in the mathematical structure behind SUSY QM. Does anybody know whether ...
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50 views

Ion-neutralization processes and its energies

Ionization energies/Electron affinities are well mapped. I wonder about opposite processes... I imagine for anion the necessary energy will be equal to the electron affinity (energy released when ...
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24 views

Multiple Entanglement

What happens when certain percentage in a group of multiple photons with same quantum state change their state. Does it affect all photons in the group or some members?
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44 views

Zero Energy States in 2D Systems

Since we are on a planar system (2D system) the massless Dirac equation reads $$\vec{\alpha}\cdot(\vec{p}-e\vec{A})\psi_E=E\psi_E$$ Here Dirac matrices are Pauli matrices ($\alpha^1=-\sigma^2$ , ...
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53 views

Why Green's function will diverge at the same spacetime point?

In $d+1$ dimensional quantum field theory, the 2-point Green's function will diverge at the same spacetime point when $d\geq1$. When $d=0$, $\phi(t)=q(t)$, that is the case of QM, and 2-point Green's ...
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46 views

Four-current, Induced Charge and Magnetic Flux

I'm studying Jackiw's "Fractional Charge and Zero Modes for Planar Systems in a Magnetic Field" DOI: 10.1103/PhysRevD.33.2500 but I have difficulties at some points. One of the problems is $$\langle ...
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36 views

Adiabatic approximation and time-dependent problems

I am an undergraduate physics student. I have a question in approximation methods for time-dependent problems in quantum mechanics. I read the proof of the adiabatic theorem but I didn't understand ...
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46 views

Angular momentums addition in QM

We know that the spatial inversion parity for eigenfunctions of $\hat {L}_{z}$ operator (spherical functions) is $(-1)^{l}$, where $l$ refers to angular momentum. So for product of two eigenfunctions ...
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49 views

What is conductivity?

I read that if we have spin $\frac{1}{2}$-particle, where a magetic force acts on, then the force is given by a drift speed times a conductivity. This conductivity is determined to be $\frac{kT}{D}$, ...
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65 views

Momentum and position operators in Schrödinger representation

I was going through some intro notes on path integral (for QFT), and am stuck with this equation for position and momentum in Schrödinger (position) representation, $$ \hat{1} =\int ...
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60 views

Does nonlocal theory violate causality?

Let's talk about two kinds of nonlocal theories. The first one frequently derives from integrating out part of the degrees of freedom to obtain a kind of effective theory. Probably, we get an integral ...
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89 views

A few questions about interacting quantum field?

In interacting quantum field, we think that interaction is adiabatic switch on/off. So in the infinite past, we can think there is no interaction, so we can have particle interpretion. There are four ...
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37 views

Quantum fluctuations in the non-relativistic limit

Is there any way to describe quantum fluctuations in ordinary quantum mechanics? For instance, a proton fluctuating into a proton-$\pi^0$ state and then back to a proton? What are the relevant ...
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19 views

Uncertainty principle characterizing metallic bonding?

So I was trying to think through the statement that the uncertainty principle can characterize metallic bonding. I know that the uncertainty principle is: $\Delta p \Delta x = \frac{\hbar}{2}$. And ...
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61 views

Variational principle

In the LMTO method, the interstitial region is approximated by plane waves and the muffin tin region of the potential by solutions to the radial Schrodinger equation. In using the variational method ...
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43 views

How does $\bar{r}\times(\bar{\nabla}\times) - \bar{\nabla}\times(\bar{r}\times)$ relate to the orbital angular momentum operator?

When I attempted to calculate the following by hand $$\bar{r}\times(\bar{\nabla}\times\bar{F}) - \bar{\nabla}\times(\bar{r}\times\bar{F}),$$ I noticed some of the terms I extracted looked similar to ...
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41 views

Why cannot we apply perturbation theory in Born-Oppenheimer approximation

In Weinberg's Lectures on Quantum Mechanics, he mentions Unfortunately, we cannot simply use first-order perturbation theory, with $T_{nuc}$ taken as the perturbation and the state vectors ...
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40 views

Quantum Excitations

In the context of quantum field theory, is the schrodinger or dirac equation actually describing some sort of an actual wave in some field like light in EM field ? So all particles are actually waves ...
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39 views

How do I properly express adding perturbed states to unperturbed states?

I have a problem set due tomorrow, and the last problem is driving me nuts. Been combing through griffiths trying to find similar examples to no avail, so it'd be greatly appreciated if stackexchange ...
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106 views

Is non-relativistic quantum field theory equivalent with quantum mechanics?

Related post Can we "trivialize" the equivalence between canonical quantization of fields and second quantization of particles? Some books of many-body physics, e.g. A.L.Fetter and ...
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21 views

Effective Spin Interaction in Helium

My question is: what is the point of forming an effective spin-spin interaction for the exchange term in the variational analysis of Helium? Is there any significance to this term other than on ...
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22 views

Conduction and propagation

What is the difference between conduction of electric wave in conductor and propagation of electromagnetic wave in dielectric? Why propagation term is used for dielectric and conduction for ...
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33 views

group velocity VS probability current

Think about an electron been accelerated from rest in a static electricfield. If we treat the problem classically, in which the electron is just a point charge. The velocity of the electron would ...
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28 views

How does a complex wavefunction “hold” energy?

Feynmann Lectures Vol 3 Ch 8 Sec 6 describes how an ammonia molecule can have two definite energy states. If the amplitudes of the base states are $ C_1(t) ...
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40 views

Coherent State in 2 dimensions

I am looking at a 2D harmonic oscillator $$H=\frac{1}{2m}(p_x^2+p_y^2)+\frac 12m(\omega_x^2x^2+\omega_y^2y^2)$$ Where $\omega_x=5\omega_y$. I am told that the oscillator is prepared in a coherent ...
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42 views

Orbital angular momentum selection rules for three identical particles

I'm trying to figure out if there are selection rules for the total orbital angular momentum for a system of three identical particles, say bosons. For two identical bosons one can argue that the ...
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65 views

Partition Function of a three state particle system

I've just finished studying the partition function of a two-state particle system, where particles can have a 0 energy value or E energy value . That is: Where $t_j$ is a variable of value ...
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92 views

Interpretation of $\langle p \rangle (t)=0$

If for a quantum mechanical particle $\langle p \rangle(t)=0$ at all time t, in any state $|\psi(t)\rangle$, can I interpret this as the center of mass of the system remains stationary? EDIT: Is ...
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29 views

spread of fock state distribution and infinite revival time of rabi oscillation in spontaneous emission

In cavity QED for a 2-level atom, the revival time for oscillation b/w the states $\left|\ e\ 0\right\rangle$ and $\left|\ g\ 1\right\rangle$ (absorbing the same photon that is emitted) is said to be ...
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41 views

POVM positive density matrix decomposition

I have to prove that given a density matrix $\rho$ in a finite d-dimensional Hilbert space $\mathcal{H}_d$, it always exists at least one informationally complete POVM measure $\{E_i\}_{i=1}^{d^2}$ ...
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70 views

Can (quantum) angular momentum $L$ be zero?

I am trying to calculate the orbital magnetic moment, $\bar{\mu}$, for Sodium, which has an electron configuration of $1s^2 2s^2 2p^6 3s^1$. The full shells do not contribute to $\bar{L}$ and ...
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47 views

Electrostatic potential of a proton

I have been working on a quantum mechanical problem regarding the ground state of the Hydrogen atom. It appears that the best way to solve the underlying problem is to modify the electrostatic ...
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72 views

Particle in a higher-dimensional box with an attractive delta potential

Suppose you have a particle in the box $[0,L]^d$, with an attractive Dirac delta potential $-\delta_{\vec w}(x)$ at $\vec w$. How do you solve the Schroedinger equation for this system? In the case ...
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37 views

Fine grained vs. coarse grained measurements and MWI

Alright, so it is my understanding that the idea that measuring systems do a coarse grained measurement which give the appearance of decoherence. I understand that the claim implicit there is that ...
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42 views

Non-locality and topology

This is a purely speculative question: Has there been any work that describes non-locality/entanglement in QM by using exotic topologies in configuration space? The 'conceptual' picture that I have ...
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48 views

What does it mean for the Leggett Inequality to falsify realism in general in Quantum Mechanics?

http://en.wikipedia.org/wiki/Leggett_inequality As you can see in the above link, it claims that Bell's inequality ruled out local realism in quantum mechanics, and the violation of Leggett's ...
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132 views

Explanation for the physics behind magnetic monopoles?

Ok so I am looking for a simple explanation of how the process is done from the information I could access and the knowledge I was allowed I have the idea that it is a matter of quantum physics and ...
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121 views

How do I write the Hamiltonian for a 3-level system?

I came across following types of three-level systems like V-system, Λ-system and 2-photon absorption It seems that their Hamiltonians can be written intuitively by checking out the coupled levels ...
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76 views

Confused by Many-Body Formalism: Creation/Annihilation to Field Operators

I'm going through an introduction to many-body theory and I am getting tripped up on the formalism. I understand quantities such as $\hat {N} = ...
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190 views

s-wave, p-wave or d-wave collisions in scattering theory

In scattering theory, what is a good intuitive picture to think of s-wave, p-wave or d-wave collisions ? What is their importance and what are the examples where a particular one is assumed to be the ...
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45 views

Falling to closest quantized circulation level in a rotating superfluid

To make a superfluid rotate in an annulus shaped container, we start with a normal fluid, rotate the container, then cool it to below critical temperature to get a rotating superfluid. The allowed ...