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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What is the difference between a photon and a phonon?

More specifically, how does a wave-particle duality differ from a quasiparticle/collective excitation? What makes a photon a gauge boson and a phonon a Nambu–Goldstone boson?
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283 views

Einstein and vibrational energy of the atom and its way to QM

As suggested by one of the commentators on my last question, I am going through Bohr's Nobel prize lecture in order to understand how quantum mechanics was developed. The lecture describes Planck's ...
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2answers
307 views

Does this Bell's experiment actually disprove Local Hidden Variable Theories (LHVT)

I'm watching some archived video lectures on QM in Coursera given by Umesh Vazirani from UC Berkeley and I have a question regarding a Bell's experiment (I guess something close to this) described in ...
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3k views

Don't understand the integral over the square of the Dirac delta function

In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being $$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$ (cf. last formula on ...
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253 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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1answer
564 views

Why do we want to entangle qubits?

The title is pretty much all I want to ask. Why are qubits entangled? To my knowledge (which isn't that deep) a quantum register can be realized without entangling the qubits.
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1answer
850 views

What is the Hubbard-Holstein model?

Please explain as simply as possible what the Hubbard-Holtstein model is and what it is used for.
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4answers
372 views

What entities in Quantum Mechanics are known to be “not quantized”?

Since all the traditional "continuous" quantities like time, energy, momentum, etc. are taken to be quantized implying that derived quantities will also be quantized, I was wondering if Quantum ...
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212 views

Introduction to quantum mechanics [duplicate]

Possible Duplicate: Book recommendations What is a good introductory book on quantum mechanics? I intend to learn quantum mechanics . But I don't have any suggestions about good books to ...
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1answer
182 views

Measurement of topological spin

How do you measure the topological spin of an anyon? So how could an experimental setup look like? Is topological spin an observable at all?
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1answer
240 views

Simulating the evolution of a wavepacket through a crystal lattice

I am interested simulating the evolution of an electronic wave packet through a crystal lattice which does not exhibit perfect translational symmetry. Specifically, in the Hamiltonian below, the ...
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2answers
383 views

When you apply the spin operator, what exactly is does it tell you?

The example I'm trying to understand is: $ \hat{S}_{x} \begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}} \end{pmatrix} = 1/2 \begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}} ...
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1answer
226 views

Equivalent Representations of Clifford Algebra

I'm reviewing David Tong's excellent QFT lecture notes here and am a little confused by something he writes on page 94. We've considered the standard chiral representation of the Clifford Algebra, ...
2
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2answers
160 views

In a double slit experiment are any particles lost because they hit the space between the two slits?

In its wave-form a particle should pass through every time because it propagates in all directions. So there shouldn't be any losses of particles landing in between the slits, right?
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475 views

Was uncertainty principle inferred by Fourier analysis?

I would like to know: did Heisenberg chance upon his Uncertainty Principle by performing Fourier analysis of wavepackets, after assuming that electrons can be treated as wavepackets?
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89 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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4answers
505 views

Why, for a spin-½ particle, are the possible outcomes of measuring spin projection along any direction the same?

If one measures the projection of spin of a spin half particle along the $x$ axis one will always get $\pm\tfrac12\hbar$. Measuring it along the $y$ axis one will always get $\pm\tfrac12\hbar$. ...
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2answers
199 views

Reference request for the Aharonov-Bohm effect

I am looking for a good reference to an online source or book, on the magnetic Aharonov-Bohm effect. I have read the appropriate sections from the book by Griffiths and Ballentine, and still haven't ...
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1answer
919 views

A Short way to show Conservation of Quantum Laplace–Runge–Lenz Vector?

I had been asked to prove the conservation of Quantum Laplace–Runge–Lenz Vector: ...
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3answers
3k views

Simple explanation of Quantum Zeno Effect

I'm a student and I had to give a talk on seminar about Quantum Zeno effect and Anti-Zeno effect to my colleagues (all listeners have had a course in quantum physics, but not a heavy one with all the ...
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1answer
494 views

What are the 't Hooft papers about classical models underlying QM?

Gerard 't Hooft states on his webpage: I have mathematically sound equations that show how classical models generate quantum mechanics. Also, there are some interesting discussions here on ...
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560 views

What is the experiment where subatomic particles appear to foresee the future?

I've seen a documentary, whose name I don't remember but I'm curious because it suggests that subatomic particles are able to "foresee the future". I'll try to describe it here: Some particles are ...
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1answer
525 views

Classical vs. Quantum use of the spin 4-vector

I have a few basic questions about the Pauli-Lubanski spin 4-vector S. I've used it in quantum mechanical calculations as an operator, that is to say each of the components of S is a matrix operator ...
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1answer
545 views

exponential potential $ \exp(|x|) $

For $a$ being positive what are the quantisation conditions for an exponential potential? $$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$ with boundary conditions $$ y(0)=0=y(\infty) $$ I ...
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2answers
274 views

Definition of “Quantizing”

Could anyone explain to me what "quantize" means in the following context? Quantize the 1-D harmonic oscillator for which $$H~=~{p^2\over 2m}+{1\over 2} m\omega^2 x^2.$$ I understand that the ...
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1answer
151 views

Can you tell if a particle is in superposition?

This may be an easy answer for anybody. Is it possible to detect if a particle A is still in a superposition via the sending a group of particles B through a box containing particle A?
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1answer
221 views

Wigner's friend and quantum Zeno effect

Suppose Winger's friend is placed into a black box, thoroughly isolated from the outside world. He constantly observes an atom with a delay of some microseconds. According to Zeno effect, atom's ...
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4answers
3k views

Amplitude of an electromagnetic wave containing a single photon

Given a light pulse in vacuum containing a single photon with an energy $E=h\nu$, what is the peak value of the electric / magnetic field?
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75 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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1answer
94 views

Noise spectrum of two systems and interacting Hamiltonian

I've been discovering recently the concept of noise spectrum, defined as: $$S_{xx}[\omega] = \int dt<x(t)x(0)>\text{e}^{-i\omega t}$$ Roughly the Fourrier transform of the two-point function. ...
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3answers
1k views

Fermi's Golden Rule and Density of States

I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
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2answers
233 views

Interpretation of $e|\psi|^2$ as electron density

In solid state physics the electron density is often equated to $e|\psi|^2$. However, the Sakurai says (Chapter 2.4, Interpretation of the Wave Function, p. 101) that adopting such a view leads "to ...
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2answers
1k views

What's the physical significance of the inner product of two wave functions in quantum region?

I am a reading a book for beginners of the quantum mechanics. In one section, the author shows the inner product of two wave functions $\langle\alpha\vert\beta\rangle$. I am wondering what's the ...
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votes
3answers
226 views

Is $k_B \rightarrow 0$ the classical limit of stat. mech., as $\hbar \rightarrow 0$ is in QM?

I hear very often among my peers and seniors that just as how $\hbar\rightarrow0$ takes me to classical mechanics from quantum mechanics, $k_B\rightarrow0$ will take me to classical thermodynamics ...
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349 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 ...
7
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1answer
358 views

Operator Ordering Ambiguities

I have been told that $$[\hat x^2,\hat p^2]=2i\hbar (\hat x\hat p+\hat p\hat x)$$ illustrates operator ordering ambiguity. What does that mean? I tried googling but to no avail.
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3answers
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Schrodinger's equation (explanation to non physicist)

For a report I'm writing on Quantum Computing, I'm interested in understanding a little about this famous equation. I'm an undergraduate student of math, so I can bear some formalism in the ...
5
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1answer
149 views

Constructing the space of quantum states

I want to learn how to construct spaces of quantum states of systems. As an exercize, I tried to build the space of states and to find hamiltonian spectrum of the quantum system whose Hamiltonian is ...
3
votes
2answers
490 views

Zero point fluctuation of an harmonic oscillator

In a paper, I ran into the following definition of the zero point fluctuation of our favorite toy, the harmonic oscillator: $$x_{ZPF} = \sqrt{\frac{\hbar}{2m\Omega}} $$ where m is its mass and ...
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1answer
840 views

Adjoint of momentum operator

In position basis, we have, $$\langle x \mid \hat p \mid \Psi(t) \rangle = -\imath \hbar \frac{\partial{\langle x \mid \Psi(t) \rangle}}{\partial{x}} $$ Now i know $\hat{p}$ is a hermitian operator ...
5
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1answer
235 views

Expectation value calculation for a weird operator

In the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups.- E weinberg I am not being able to see one of the calculation. The author states (eqn 3.26) $$\langle ...
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1answer
339 views

Does a particle in a spherically symmetric infinite square well potential exert a force on the inner and outer shell barrier?

For a particle in the potential: $$V(r) = \begin{cases} 0 & \text{a < r < b}\\ \infty & \text{otherwise.} \end{cases}$$ Does this guy in the ground-state exert a force on the shells a ...
2
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0answers
205 views

How to calculate radiative transition rate of exciton in a quantum dot with specific dimension?

I am writing rate equations for a nanophotonic system including three quantum dots. I need to calculate that radiative transition rates of exciton in ground state in those quantum dots. In the paper ...
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2answers
444 views

Angular Momentum Operators Non-Degenerate

Typically one writes simultaneous eigenstates of the angular momentum operators $J_3$ and $J^2$ as $|j,m\rangle$, where $$J^2|j,m\rangle = \hbar^2 j(j+1)|j,m\rangle$$ $$J_3 |j,m\rangle = \hbar ...
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2answers
562 views

A thought experiment with Heisenberg's Uncertainty Principle [duplicate]

Possible Duplicate: Could the Heisenberg Uncertainty Principle turn out to be false? Thought Experiment Ponder, for a moment, if I had a cube with 10cm sides which I'll name The Box. By ...
6
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4answers
4k views

How do electrons jump orbitals?

My question isn't how they receive the energy to jump, but why. When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals ...
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2answers
397 views

WKB method of approximation

Would it be legitimate to use the WKB approximation for a particle in a spherically symmetric Gaussian potential? $$V(r)~=~V_0(1-e^{-r^2/a^2}).$$ I'm not sure when to use which approximation ...
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90 views

Quantum Conservation versus classical conservation

If energy is conserved in all quantum mechanical interactions, how are there classical interactions in which energy is not conserved, given that classical interactions are a macroscopic approximation ...
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2answers
481 views

Double slit experiment alternating holes

If we perform the double slit experiment by shoting photons covering one hole at a time, would we see equally the double slit interference?. That is, the same set up of double slit but fire photons ...
2
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1answer
139 views

Potential of particle exchange

There are two heavy particles (of mass $M$) and a light one (of mass $m<<M$). The light particles interact with heavy particle with an attracting dirac delta potential ...