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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61 views

What is negative probability? [duplicate]

I am going through Quantum Computing, and thought to clear the basics first. So, I read blogs on Quantum Mechanics. They mention about Negative Probability. Now, what is that, this is very new to me. ...
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1answer
83 views

How do you add angular momentum of three or more particles in quantum mechanics?

I'm trying to find some information on how to add the angular momentum of three or more particles, but all the sources I look at deal with only two. In this case I understand that if the angular ...
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2answers
149 views

Isomorphism of rigged Hilbert spaces

In connection with the statement that QM can be formulated in terms of separable complex (rigged) Hilbert spaces, the fact that all infinite dimensional separable complex Hilbert spaces are isomorphic ...
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69 views

Derivation of Rashba spin-orbit coupling in tight-binding model

Rashba spin-orbit coupling Hamiltonian in free space can be written as: $H_{\text{so}}=\int d^3r \Psi^{\dagger}(\mathbf{r}) \gamma (p_{x}\sigma _{y}-p_{y}\sigma _{x})\Psi(\mathbf{r})$. I expand ...
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1answer
69 views

Problem in understanding matter wave

Matter wave is the wave associated with a particle having momentum $p$ ; its wavelength being $$\lambda = \dfrac{\mathbf{h}}{p}$$. So, particle moving with high momentum has lower wavelength. Ok, upto ...
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20 views

Are the Wigner and Husimi transforms injective?

I am wondering if the Wigner function is injective. By injective I mean, that, for every density matrix $\rho$, there is a different Wigner distribution. The same question applies to the Husimi ...
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1answer
78 views

Does it make sense to define the mean free path in quantum mechanics?

The mean free path defined in classical molecule dynamics has a strong classical flavor. Is it sensible to generalize the idea to quantum mechanics?
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1answer
24 views

Fermi distribution and ideal gas

I was wondering about the following: If we have ideal gas particles, then $E \ge 0$, so one would expect that the state $E=0$ is occupied with probability one for low temperatures, but this is not ...
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36 views

What is the missing step in this result regarding the creation operators in Fock space?

In the above extract from Simons and Altman: Condensed Matter Field Theory, I am having trouble getting from (2.3) to (2.4) in the case of Fermions (ζ=-1 and the n(subscript i) values are modulo 2). ...
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25 views

What is the limit of directly detecting a resonance?

Some resonances are extremely short-lived. With a lifetime of $10^{-23}$ seconds, they would travel just about the size of the proton ($10^{-15}$ m) even if they traveled at the speed of ...
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22 views

Do electrons of different energy levels have different wave equations if they are all in the ground state?

I am supposed to consider 6 free electrons in a dye molecule as 6 electrons in a potential well of width 1 nm (making the infinite well approximation). The question asks: "Calculate the net charge ...
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3answers
59 views

How are Superposition and Entanglement related?

How are Superposition and Entanglement related? I don't know much of Quantum Mechanics. I am CSE student and got started with this Quantum Computing. It is interesting! If anybody can help me on ...
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1answer
158 views

Proof of weaker Baker-Campbell-Hausdorff Formula [duplicate]

Prove the weaker form of the BCH Formula: $$e^A e^B = e^{A + B + \frac{1}{2}[A,B]} $$ with the assumption $[A, [B, A]] = 0; [B, [B,A]] = 0$ Start with $f(\lambda) = e^{\lambda A} e^{\lambda B} ...
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27 views

Showing a measurement operator has a particular form

I came across an exercise (Ex 1.16) in 'Quantum Measurement and Control' by Wiseman and Milburn that I am having some trouble with. Suppose we have some system $S$ coupled with two meters in states ...
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37 views

finetuned quantum experiments by Murch lab, do any have dynamics outside of basic QM formalism/ axioms?

a series of very finetuned quantum experiments have been reported by the Murch lab eg in 2 articles in Nature & analysis there,[1][2][3] some leading to dramatic accounts in the media.[4] do ...
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2answers
94 views

Does Bell's theorem rule out the possiblity that measurements are completely determined by events in the past light cone?

I'm studying Bell's theorem and the CHSH inequality for some time. Now it's clear to me that one cannot reproduce the correlations predicted by quantum mechanics by assuming that particles carry ...
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1answer
43 views

Would a pair of independent quantum coin tosses be perfectly anti-correlated?

Background Suppose we attach a button to an electronic flip flop such that an LED will toggle when we press the button with 50% probability, where the source of the randomness is a quantum event, ...
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1answer
202 views

Why does the wave function have to be continuous? [duplicate]

When solving one dimensional problems in quantum mechanics it is often assumed that the first derivative of the wave function is contineous. What justifies this assumption?
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3answers
144 views

Can existing quantum computers be considered evidence for parallel universes?

In this video ( http://www.youtube.com/watch?v=bJpIclDmi2M ) Max Tegmark , a MIT cosmologist says that if we build a quantum computing successfully it will be a evidence that Parallel Universes ...
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0answers
25 views

Are electrons matter waves? [duplicate]

While studying the de Broglie equations today I learned that electrons are particles that also act as matter waves. But in my text book I learned that there is a mathematical equation that says that ...
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1answer
37 views

Scaling of an eigenvalue with the coupling constant

Consider the Hamiltonian $H = - \frac{d^2}{dx^2}+gx^{2N}$. Scaling out the coupling constant $g$, the eigenvalues scale as $\lambda \propto g^{\frac{2}{N+2}}$. So, we can drop the g dependence and ...
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2answers
126 views

Wave functions as $x$ goes to infinity

This problem emerged when I was going through some QM exercises: I've been asked to find the commutator $[A,B]$ where $A,B$ are defined as $$A\psi(x)=x\frac{\partial }{\partial x}\psi(x),$$ ...
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1answer
34 views

Using attosecond laser pulses to view electrons

It is often said in popular media sources that creating shorter and shorter laser pulses will allow us to view electron dynamics as they happen in chemical reactions. This is obviously beneficial in ...
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13 views

The Wigner 3j-Symbol and Kronecker delta

If you look up the definition of the Wigner 3j-Symbol (e.g. on Wolfram) you'll find $m_1+m_2=M$ must be satisfied. Does that mean that, for an arbitrary Wigner 3j-Symbol I could replace: $ ...
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2answers
118 views

What is the connection between geometry of physical space and Hilbert space?

In Quantum Mechanis (QM), the dynamical variables are the (quantized) coordinates $x_j$ and their canonical conjugate $p_j = -i\partial_j$ with the commutation relation $[x_j,p_k]=i\delta_{jk}$ ...
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1answer
28 views

Reducing unitary evolution operator of a two-spin system to the evolution operator of one of the spins

Consider a system of two spins $s_1$ and $s_2$, each of which can be in one of two states, represented by 0 or 1. A basis for the Hilbert space of this system would be {|0,0>,|0,1>,|1,0> and |1,1>}, ...
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1answer
66 views

Harmonic oscillator problem - Griffiths [closed]

I'm solving problems about harmonic oscillator from Griffiths book (2nd ed.) and I'm stuck in the problem 2.13. When I normalize the equation 2.51 to get $A_1$ my final wave function is complex, since ...
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1answer
38 views

On quantum randomness, the longest weather predictions and perfect macroscopic caos

Which is the maximum number of days we can predict future weather conditions with a reasonable degree of accuracy if we knew all of the initial conditions of everything that effects the weather down ...
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1answer
60 views

If I want to determine a particle's momentum or position, do I get this information from the wave function?

I am confused about how one measures the dynamical variables (eg position) of a particle. I thought the wave function $\Psi(x,t)$ was the probability amplitude and $|\Psi(x,t)|^2$ represents the ...
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0answers
35 views

Conjugate of unknown qubit?

I have seen this problem somewhere on stack exchange, but I have a separate question. Given a qubit which is unknown say $\alpha|0\rangle +\beta|1\rangle $ ( $\alpha, \beta$ are unknown ) is there a ...
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1answer
29 views

Wigner-Yanase skew information [closed]

I am reading Eric Carlen's paper on Trace Inequalities and Quantum Entropy. I am currently reading about the Wigner-Yanase skew information which is defined as: $$I_{WY}(\rho)=-\frac{1}{2} ...
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1answer
48 views

How do I properly calculate the curl of the Aharonov-Bohm flux line vector potential?

Given a vector potential describing an infinitely thin line of flux, $$\vec{A} = \frac{\Phi}{2\pi r} \vec{e}_\varphi,$$ How can I calculate the curl so that the magnetic field is given by $$\vec{B} ...
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4answers
232 views

What is the energy of a superposition of energy eigenstates?

$\newcommand{\ket}[1]{\lvert #1 \rangle}$Suppose I have a system say SHO in a superposition of energy eigen states $\ket{n_1}$ and $\ket{n_2} $ given by $\ket{\psi} = \frac{1}{\sqrt{2}}\ket{n_1} + ...
1
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1answer
86 views

What are the electromagnetic fields of a photon?

I'm looking for expressions for the electromagnetic fields (preferably $E$ and $B$) of a typical photon which is localised in space to some extent (i.e. I'm not interested in the infinite plane wave ...
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1answer
91 views

How to prove that the position operator in momentum is $i\hbar \partial/\partial p$ - One Missing Sign

I am trying to prove that the position operator in momentum space is $i\hbar \partial/\partial p$ but my derivation is missing one sign. Can someone spot the error? Start with $$<\hat x> ...
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0answers
26 views

Commutator for time?

I know that in quantum mechanics, we can define space as the operator $\hat{x}=i\hbar \frac{d}{dp}$ in momentum space,and that position does not commute with momentum. However, in general relativity, ...
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2answers
125 views

What is the difference between a bit and a qubit?

I am Computer Science student and learning about quantum computing. But, I have a problem in understanding Bit and Qubit relationship. A bit with 2 bits = 4 states 00,01,10,11--- 1 state at a time. ...
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3answers
97 views

What “is” energy in sub-atomic particles?

This question may be simple or not, I don't know but I can't find the answer anywhere. The electromagnetic spectrum is the range of light particles in different wavelengths and is supposed to be ...
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1answer
32 views

Dealing with tensor products in an exponent

I am looking at the following problem and I am struggling to follow the steps involved. Consider the non-interacting Hamiltonian $$H_{AB}=H_A\otimes I_B+I_A\otimes H_B$$ So I'm trying to prove that ...
10
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3answers
255 views

Can spin-1/2 emerge as a property of quasiparticles if original description of the system was without spin?

When we consider a band structure of some crystal, we can get a model of particle-antiparticle system like electrons and holes. In graphene, for instance, we even get a model of massless Dirac ...
2
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1answer
101 views

How do sharp time intervals arise in a mesoscopic/macroscopic system?

$\newcommand{\ket}[1]{\left|#1 \right\rangle}$ $\newcommand{\bra}[1]{\left\langle #1 \right|}$ For a physical process in a mesoscopic/macroscopic system, how exactly can one deduce the time that ...
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1answer
62 views

In what sense are photons emergent?

Recently I read in an essay by Wilczek: "Photons are mixtures of weak B3 and hypercharge C mesons. It is those objects, not the emergent photon, whose properties are ideally simple." Until now I ...
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2answers
203 views

An identity of Pauli matrices

I am studying spin recently, and textbook gives some identities of Pauli matrices, one said that for any two unit vectors $\bf m$ and $\bf n$, $[\bf m \cdot \bf{\sigma},\bf {n \cdot \sigma}]= ...
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32 views

Gedankenexperiment to derive the Robertson uncertainty relation without confusing it with the obersver effect

In the last years there seemed to be much activity on the meaning Heisenberg's uncertainty relation. The main point of the discussion was Heisenbergs noise-disturbance-relation (see: ...
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114 views

Position and momentum expectation values for the stationary states of the infinite square well [closed]

I'm really lost in figuring out how to solve the integral for the expectation value of $x$ and $x^2$ $$\int_0^a x \sin(\frac{n\pi}ax)^2 dx $$ This equation is from the $n$th stationary state ...
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4answers
85 views

Energy of a wave and Planck formula

Especially from this post I understand that the energy of a wave is directly proportional to the amplitude of that wave squared. Therefore, we can determine the total energy of a wave by summing the ...
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1answer
38 views

What is the sum over the transition rates?

I was looking at the solution to an exercise, and I came over this expression: $$P_{i\to f} = \sum \limits_{f} {2 \pi \over \hbar }\; |\langle f |\hat V | i \rangle |^2 \delta(E_{fi}-E),$$ where ...
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1answer
48 views

Losing a term for 3D radial schrodinger equation

I am trying to solve the Schrodinger equation For a potential $V(r)$ defined for $ 0<r<R$ as $$V(r)=-V_0 $$ and zero everywhere else. For wavefunction $u$ I can easily get to $$ u'' =-k^2u,$$ ...
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23 views

representation of spinors

I am trying to get from the abstract representation of Spinors, as wave functions $|\Psi \rangle$ in the base of tensors products $| S_z \rangle \otimes | x \rangle$ of eigenvectors of the spin ...
2
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1answer
70 views

What am I REALLY doing when I take the Fourier transform of the momentum operator

I was playing around with some equations and found a surprising relationship when I took the fourier transform of the momentum operator Define $\hat P = \frac{\hbar}{i} \partial_x$, then $F(\hat P) = ...