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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Photoelectric effect and evanescent fields

We all know that if light impinges upon a metal and if it's the energy of the photon (hv) is greater than the work function of the metal then an electron will become unbound from the metal and be ...
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1answer
199 views

Using open system dynamics to define a quantum state

Background The density matrix of a closed quantum system with Hilbert space $\mathscr H$ evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a ...
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158 views

why the Laughlin's wave function is an incompressible quantum state?

some comments about the meaning of an incompressible quantum liquid are posted here: Incompressible quantum liquid In the same context, the Laughlin's wave function for a filling factor of 1/3 ...
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2answers
73 views

Can quarks have anti-colors?

I get the basics of QCD (or I think I do). What I was wondering is whether up and down quarks, and their heavier cousins, absolute HAVE to carry color charges, or if they can have anti-color charges ...
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2answers
39 views

Selection rules and type of photon?

Let us consider the following matrix element: $$\langle n',m',l'|x| n, m, l \rangle$$ For the corresponding radiative transition we have the selection rule that $\Delta m=\pm 1$. But will the photon ...
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25 views

Expectation value in second quantization

I am stuck calculating a simple expectation value for an operator, which is expressed in second quantization. I know the result, but I fail to proof it. Lets say I have one-particle wave function ...
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7answers
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+350

Why is the application of probability in QM fundamentally different from application of probability in other areas?

Why is the application of probability in quantum mechanics (QM) fundamentally different from its application in other areas? QM applies probability according to the same probability axioms as in other ...
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36 views

Wavefunctions “adapted” to the perturbation ? Relation to Faraday effect

I came accross the following statement in a book: If one wants to switch on a magnetic field, one must first choose the appropriate complex unperturbed wave functions (that are "adapted" to the ...
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1answer
40 views

Calculating eigenvalues for operator [on hold]

Given relation $[a,a^\dagger]=I$. Operator $K$ is defined as $K=a^\dagger a+\lambda a^\dagger+\lambda^* a$. I need to find the eignevalues of operator $K$. How realtion that involves commutator could ...
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1answer
106 views

What is the greatest observed distance between clearly entangled particles?

As far as I can understand, decoherence will break entanglement. Given that, what is the greatest distance between entangled pairs, that has been successfully observed? Is it possible to identify ...
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13 views

Conditions for supersonic flat plate problem [on hold]

I am interested to solve "supersonic flat plate problem". I want to ask that how do conditions for this problem set?
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2answers
891 views

What is the kinetic energy of a quantum particle in forbidden region?

I have read that if a particle is trapped in a finite potential well, it has a finite chance to tunnel out from it. Therefore, one can find a particle in a region where its potential energy is greater ...
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1answer
40 views

What is an incoherent state?

I am reading through a recent paper which speaks frequently of "incoherent states" without ever defining what such a state is. I gather from the context of the paper that it has something to do with ...
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2answers
66 views

Does Unitary operator take a pure state to a pure state or can it take a pure state to a mixed state?

Does Unitary operator take a pure state to a pure state or can it take a pure state to a mixed state? I think so but why? I assume the Unitary operator acts on a pure state only.
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1answer
61 views

Schroedinger and Klein-Gordon equation and their complex conjugate

Let's consider the Schroedinger equation \begin{equation} i\hbar\frac{\partial}{\partial t}\psi=-\frac{\hbar}{2m}\nabla^2\psi \end{equation} If I have a wavefunction $\psi$ as a solution, then its ...
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1answer
119 views

Angular Momentum of a Photon

Why is it that the angular momentum of a photon is $\hbar$, irrespective of its energy? I encountered such a claim in a text about Raman spectroscopy. Is there an explanation for this using basic ...
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51 views

Wavefunction of electron in 3D infinite well with non-zero potential

Consider an electron moving in a potential $V$ defined by $$V(x,y,z) = \left \{ \begin{array}{ll} \alpha(x^2 + y^2) & 0 \leq z \leq a \\ \infty & \text{otherwise} \end{array} \right. $$ ...
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1answer
127 views

Why is the unitary matrix relating the gamma matrices and their complex conjugates antisymmetical?

In Messiah's Quantum Mechanics Vol. II, properties of the Dirac matrices are derived. There is so-called fundamental theorem, which states that, Let $\gamma^\mu$ and $\gamma^{'\mu}$ be two systems of ...
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1answer
54 views

How do physicists find the speed of neutrinos?

I have heard that there is evidence for neutrinos traveling close to the speed of light, but how is that done? Since neutrinos barely react with anything, and the only evidence for them is indirect ...
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38 views

First order time-independent perturbation theory: How to practically calculate the perturbed wave-function

This is one of the problems that draws the line between academically learning something, and having to use it. While I learned the formulas relevant to this, I just want to make sure I'm using them ...
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17 views

Causal networks and “local” entanglement

On his Opus Maximus, a new kind of Science, Stephen Wolfram suggests that causal networks can create behaviour similar to entanglement because the local structure of space is only an averaged ...
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2answers
785 views

Degeneracy in one dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a potential ...
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1answer
49 views

Definition of the S-matrix

when I think about scattering process I reach to slightly another definition to the S-matrix. because I understand my reasoning I hope someone could refine it to a correct one so that I can have a ...
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1answer
54 views

Bloch sphere representation of $\sigma_x$ operator on $|1\rangle$

I am trying to visualize a Hamiltonian H=$\hat{\sigma_x}$ $$ \hat{\sigma}_{x} = \left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right) $$ acting on the state $| 1 \rangle$. I can write ...
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1answer
60 views

The $T\rightarrow \infty $ limit in quantum field theory

I am new to quantum field theory. Prior to this, I have been using quantum mechanics for a few years. I am reading the book by A. Zee, ''quantum field theory in a nutshell'', 2nd Ed.. On page 18, ...
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30 views

Density matrix and basis

Given an hermitian operator $\hat{A}$ I can span the Hilbert space in terms of the eigenvectors $\lvert a_i\rangle$. For example in a spin $1/2$ system I can choose to work in a basis from the ...
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1answer
108 views

Dirac delta function definition in scattering theory

I'm studying scattering theory from Sakurai's book. In the first pages he gets to the following expression: $$\langle n|U_I(t, t_0)|i\rangle=\delta_{ni}-\frac{i}{\hbar}\langle ...
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2answers
126 views

About de Broglie relations, what exactly is $E$? Its energy of what?

Well, you may know de Broglie relations, here they are: $$ E = h\nu, \quad\quad p = \frac{h}{\lambda} $$ My question is simple: What exactly is $E$? Is it the total energy? Maybe only kinetic energy? ...
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44 views

Sum rule and dense limit

Is the finite size of lattice constant important for derivation of sum rules, for example, the sum rule for diagonal conductivity $\sigma_{xx}$: $$ \int \limits_{-\infty}^{\infty} ...
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4answers
2k views

Is the statistical interpretation of Quantum Mechanics dead?

I'm sure this question is a bit gauche for this site, but I'm just a mathematician trying to piece together some physical intuition. *Question:*Is the statistical interpretation of Quantum ...
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23 views

Are there explicit formulas for the eigenvalues and eigenvectors of a generic 4x4 density matrix? [migrated]

I have a 4x4 density matrix all of whose elements are nonzero. Its form is $$\begin{pmatrix} a & b & c & d \\ b^* & e & f & g \\ c^* & f^* & h & j \\ ...
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1answer
41 views

Different postulates and statistical interpreations of quantum mechanics

Hi I have a query about the difference of two aspects of the statistical interpretation of quantum mechanics given in the popular introductory quantum mechanics books "Introduction to Quantum ...
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1answer
194 views

Quantum mechanics, what's possible?

There is a thread in Physicsforums.com which states due to Quantum Mechanics, if you wait long enough diamonds will appear in your pocket, it also states it's possible for all your atoms to ...
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1answer
45 views

Scattering in Schrödinger picture [on hold]

If we look at a scattering process in the Schrödinger picture for a Hamiltonian $H = H_0(t) + V(t)$ where $H$ is independent of time (because we examine a theoretical situation after accelerating ...
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29 views

Non-locality Vs deterministic correlated states [on hold]

Take this scenario: 2 pair were entangled (P1,P2) Take P2 and entangle it with P3 Destroy P2 Now we have P1 & P3 correlated although they never met each other. P2 transferred it's ...
4
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1answer
52 views

Schrödinger-Pauli Equation Solutions

The Schrödinger-Pauli equation is the non-relativistic limit of the Dirac equation, and therefore describes spin-1/2 particles in an external electromagnetic field. It is given by: ...
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1answer
176 views

How can energy be negative in a finite square well?

Say if the potential $V(x) < 0$ in the well but the sides or the scattered states its zero potential, anyways How is that the energy in the well is less than zero? Is it because the potential ...
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72 views

The Madelung Equations are Euler Equations for Quantum Mechanics. What is the Lagrangian description of Quantum Hydrodynamics?

The Madelung Equations of Quantum Mechanics suggest the Hydrodynamic Model of Quantum Mechanics (Quantum Mechanics is described as a fluid of universes in a multiverse, which, in the non-relativistic ...
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2answers
271 views

Specific heat capacity and temperature, 0 K?

I've found similar threads like this, but with no clear answer. I understand that the specific heat capacity of a substance increases with temperature, because the vibrational nodes and rotational ...
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0answers
53 views

Quantum mechanics: Path integrals vs normal

What are the similarities and differences in the theory for quantum mechanics using path integrals versus the normal method using wave functions?
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2answers
240 views

Doppler effect of matter waves

We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object. We also know the the concept of particle-wave ...
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1answer
64 views

Spacetime background of Quantum mechanics [on hold]

Why is it said that the Schrodinger equation suggests a fixed, non-dynamical background spacetime, with time as an external parameter? How does this interpretation come about from the Schrodinger ...
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0answers
44 views

Basic quantum entanglement reference

What basic (first course for undergrads) quantum mechanics book would you recommend to read about entanglement?
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2answers
139 views

Why the cross section can be obtained directly from the stationary scattering states?

I'm currently studying scattering theory in the book Quantum Mechanics, Vol. 2 by Cohen-Tannoudji. In the book the author deduces that to find the number of particles detected far from the target at a ...
2
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2answers
312 views

Oscillation of a Bose Einstein condensate in a harmonical trap

We were asked to try to make a theoretical description of the following phenomenon: Imagine a 2D Bose Einstein condensate in equilibrium in an harmonical trap with frequency $\omega$. Suddenly the ...
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0answers
1k views

tritium beta decay - probability of being in 1s state

Hydrogen-like wavefunctions have the form: $$R_{10} = \left(\frac{Z}{a_0}\right)^{\frac{3}{2}} 2\space e^{-\frac{Zr}{a_0}}$$ $$Y_{00} = \frac{1}{\sqrt {4\pi}} $$ where $a_0 = \frac{4\pi \epsilon_0 ...
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1answer
92 views

“Anti-classical” limit of large Planck's constant

A central theme in quantum physics is the classical limit where $\hbar \rightarrow 0$, and there is lots of interesting structure to this limit (i.e. classical mechanics). Is there anything ...
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1answer
40 views

Meaning of non diagonal terms in decoherence

It is my understanding that the non-diagonal terms in the density matrix of a macroscopic system that it is initially in an entangled state go exponentially fast to zero as the system interacts with ...
7
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2answers
100 views

How can quantum tunnelling lead to spontaneous decay?

I have never understood what measuring process (if any) is supposed to be continuously polling the quantum state of an unstable bound system subjected to decay via quantum tunnelling. The reason I ...
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1answer
228 views

Thought Experiment: Force on magnets in a Stern Gerlach Experiment

Background: In the SG experiment, an inhomogenous magnetic field affects a force on particles passing between two magnets. "Measurement" takes place when a screen is placed on one end, blocking one ...