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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Polarization photon and Stokes parameters

I have the following situation: About the polarization of the photon, I introduce the basis: Horizontal polarization $|\leftrightarrow>=\binom{1}{0}$ Vertical polarization ...
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113 views

Measurement in Quantum mechanics

I have got a quantum conservative system whose Hamiltonian is $H$. I consider an selfandjoint operator $O$ whose eigenvalues and eigenvectors are: $$O|\psi _{n}\rangle = \lambda _{n}|\psi ...
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188 views

According to wave function collapse you only have one outcome, so what happens to the other superpositions?

If the superpositions of a wave function are not needed because only one of the superpositions is allowed, what happens to the eigenvalues of the "null" superpositions? Is the energy transferred ...
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85 views

Neutrino mass as counted in Dark Matter

If I try to add up neutrino masses (let's assume 1 eV rest mass equivalent each) to count as DM, do I use the rest mass or relativistic mass?
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189 views

Conformal Quantum Mechanics

I heard the term Conformal Quantum Mechanics used today. What exactly does this mean? Why would one want to study this?
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173 views

Qubit, one or two complex numbers?

I'm currently reading up on quantum computing and it seems like I have found some contradiction about how to represent qubits. It is often stated that a qubit is represented as $a|0\rangle + ...
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132 views

Transform hamiltonian

I have got the following Quantum Hamiltonian: $$H=\frac{p^{2}}{2m}+k_{1}x^{2}+k_{2}x+k_{3}$$ Which transformation can I use to change this Hamiltonian into an harmonic oscillator hamiltonian? ...
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381 views

Quantum mechanical angular momentum and spin formalism/notation

I am currently stuck on the following notation: $\frac{1}{2}\otimes\frac{1}{2} = 0 \text{ (antisym) } \oplus 1 \text{ (sym) }$ No matter what I tried, I couldn't derive the identity. I am sure that ...
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92 views

How many ways are there to distribute M excitations of N identical particles among K=3 quantum harmonic oscillators?

I'm trying to numerically calculate a partition function of N non-interacting but identical particles in a 3D SHO. To do this, I'd like to know the degeneracy of $M$ excitations, $N$ indistinguishable ...
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56 views

Length of the orbit (semiclassical orbits)

The Gutzwiller trace is about $$ d(E)=d_{0} (E)+ \sum_{p.o}A_{p}Cos(S(E)\ell_{p}) $$ and $ \ell_{p} $ are the length of the orbit. However my question is, how can one derive the length of the orbit ...
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144 views

NOT Universal Operator and Computational basis

This is the relationship between density operator and Bloch vector: $$\rho= \frac{1}{2}({\bf{\hat{1}}}+{\bf{b}}.\boldsymbol{\hat{\sigma}})$$ We define the NOT Universal Operator in the following way: ...
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350 views

Weak measurements rule out Many Worlds Interpretation?

I came across a paper that claims to prove that the Many Worlds interpretation is invalid by applying weak measurements. The paper can be found here: ...
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943 views

How does Bell's theorem rule out the possibility of local hidden variables?

It seems to be common consensus that the world is non-deterministic and this is proved by Bell's theorem. But even though Bell's experiments proved that the theory of quantum mechanics work, How does ...
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317 views

Matrix operation in dirac matrices

If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ? ...
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446 views

Elastic collisions in Franck-Hertz experiment

Looking at a Franck-Hertz experimental setup, and given a potential difference such as $4.0\ V$ which is too small to excite out the first electron orbital, the electrons moving through the tube will ...
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526 views

How is quantum mechanics compatible with the speed of light limit?

Consider a free electron in space. Let us suppose we measure its position to be at point A with a high degree of accuracy at time 0. If I recall my QM correctly, as time passes the wave function ...
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306 views

Topology and Quantum mechanics

I have a very simple question. Can we know about the topology of the underlying space-time manifolds from Quantum mechanics calculations? If the Space-time is not simply connected, how can one measure ...
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79 views

Empirical meaning of relativity in the context of QM

In special relativity an event E is mapped to coordinates (x,t) in one inertial frame, and to coordinates (x',t') in another, and SR provides the relation between (x,t) and (x',t'). What is the ...
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1k views

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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310 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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567 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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852 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
374 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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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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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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384 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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227 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, ...
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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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476 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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507 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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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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934 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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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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495 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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562 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
531 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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546 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
275 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
153 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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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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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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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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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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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 ...