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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1answer
764 views

Ground state energies with fermions of same spin?

Consider two non-interacting Fermions (half-integer spin) confined in a 'box'. Construct the anti-symmetric wavefunctions and compare the corresponding ground-state energies of the two systems; ...
1
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3answers
236 views

Quantum of Time

I am not a String Theorist, but I just want to ask if there is anything which specifies a quantum of time, as per M-theory? Can a quantity such as $$ t_p = \left(\frac{\ell_p}{c}\right),$$ where ...
2
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1answer
311 views

How is partial trace simplified?

I'm currently reading papers about the effect of repeated measurements, such as "Purification through Zeno-Like Measurements", arXiv:quant-ph/0301026 (DOI: 10.1103/PhysRevLett.90.060401). It says ...
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1answer
292 views

Seeking a specific quantum spin system of interacting spin 1/2 particles

Is there a system of interacting quantum spin 1/2 particles (of any topology) whose the states where all spins are up or down are eigenstates of its Hamiltonian and yet does not conserve the total ...
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3answers
306 views

Which are the simplest known contextual inequalities?

It is well-known that quantum mechanics does not admit a noncontextual ontological model, and there are countless different proofs of it. I'm interested in the simplest proofs that can be cast as an ...
2
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1answer
243 views

functional determinant and WKB approximation

let be a Hamiltonian in one dimension, i would like to evaluate the functional determinant $ det(E-H) $ in onde dimension i believe that $ det(E-H)= Cexp(iN(E)) $ here $ N(E)$ is the number of ...
3
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1answer
481 views

How far can you get (in quantum mechanics) with just commutation relations?

Clearly it is possible to derive a set of commutation relations from some Hamiltonian, and certainly they give useful and interesting invariants when investigating the behavior of quantum systems. ...
3
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2answers
960 views

Why did Schrodinger never budge on the meaning of $|\Psi|^2$

Schrodinger believed that the phisical interpretation of the wavefunction $\Psi$ was the vibration amplitude and $ |\Psi|^2 $ was the electric charge density. While no-one disagrees with his ...
11
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1answer
240 views

Majorana-like representation for mixed symmetric states?

Is there a generalization of the Majorana representation of pure symmetric $n$-qubit states to mixed states (made of pure symmetric $n$-qubit)? By Majorana representation I mean the decomposition of ...
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1answer
534 views

Gauge invariance and Feynman path-integrals

Let me look at the Hamiltonian of a charged particle in a plane in a constant magnetic field ($\vec{B}$) pointing upwards - then in usual notation it is, $$\hat{H} = \frac{1}{2m}\biggl(\hat{p} + ...
17
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1answer
306 views

What proof techniques have failed for solving the SIC-POVM problem and what new insights have been gleaned from them?

The SIC-POVM problem is remarkably easy to state given that it has not yet been solved. It goes like this. With dim($\mathcal H$) $=d$, find states $|\psi_k\rangle\in\mathcal H$, $k=1,\ldots,d^2$ ...
13
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1answer
202 views

Explicit construction for unitary extensions of completely positive and trace preserving (CPTP) maps?

Given a completely positive and trace preserving map $\Phi : \textrm{L}(\mathcal{H})\to\textrm{L}(\mathcal{G})$, it is clear by the Kraus representation theorem that there exist $A_k \in ...
2
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1answer
776 views

scattering theory problem

I am studying scattering theory right now in my QM class, and I'm attempting the Griffiths problem 11.4 as an exercise (it's not for homework). The problem is: Consider the case of low-energy ...
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2answers
968 views

Inverted Harmonic oscillator

what are the energies of the inverted Harmonic oscillator? $$ H=p^{2}-\omega^{2}x^{2} $$ since the eigenfunctions of this operator do not belong to any $ L^{2}(R)$ space I believe that the spectrum ...
3
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1answer
191 views

Is decoherence due to coarse graining or coupling with the environment?

In the literature, sometimes one reads that decoherence is due to the coupling of the system to the external environment, and sometimes one reads that it is due to coarse graining over the microscopic ...
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1answer
451 views

Chance of “macro tunneling”?

We know that subatomic particles can and do tunnel through barriers, so it is theoretically "possible" somewhat that a grain of sand could tunnel through a paper, but Id like to get some perspective ...
3
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2answers
293 views

What is Phase Space Forumation of QM and does it explain use of complex variables in QM?

In arXiv:quant-ph/0504102v1, A.J. Bracken says if we think of the phase space formulation of QM as more fundamental, arising directly from a deformation of classical mechanics in phase space ...
13
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1answer
190 views

What is the Holevo-Schumacher-Westmoreland capacity of a Pauli channel?

Suppose you are given an $n$-qubit quantum channel defined as $\mathcal{E}(\rho) = \sum_{i} p_i X_i \rho X_i^\dagger$, where $X_i$ denotes an $n$-fold tensor product of Pauli matrices and $\{p_i\}$ is ...
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2answers
250 views

Relevance of SIC-POVMs to quantum information

What is the real relevance of SIC-POVMs (symmetric informationally complete POVMs) to concrete tasks in quantum information theory? A lot of work has been put into giving explicit constructions, and ...
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1answer
140 views

Poles, wavefunctions, transmission

Why is it said that $\operatorname{sech}x$ (a transmission amplitude) has a simple pole on the imaginary axis?
3
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1answer
634 views

Transmission and reflection

What is the transmission amplitude of a wavefunction $\phi(x)=e^{ikx}(\tanh x -ik)$? I would have thought that it is $\tanh x -ik$ since this is the factor associated with the forward travelling ...
4
votes
1answer
486 views

What is the definition of a 2-cocycle in Quantum Mechanics

I'm having this lecture on QM and we are giving an introduction on Lie Groups. So... this week we have been talking about central extensions of LG (such as Galilean) and related to this popped up ...
3
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1answer
204 views

Expected value inequality

Why is $\langle p^2\rangle >0$ where $p=-i\hbar{d\over dx}$, (noting the strict inequality) for all normalized wavefunctions? I would have argued that because we can't have $\psi=$constant, but ...
2
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1answer
794 views

Hyperfine structure vs Lamb shift in the hydrogen atom

The hyperfine structure of the energy levels of the hydrogen atom refers to the shifts in the evergy levels due to the magnetic moments of the nucleus and of the electron. This is an effect of ...
2
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3answers
634 views

Spin decomposition in general

I can turn-the-crank and show that $\frac{1}{2}\otimes \frac{1}{2} = 1\oplus 0$ etc, but what would be a strategy to proving the general statement for spin representations that $j\otimes s ...
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4answers
2k views

What is the fundamental probabilistic interpretation of Quantum Fields?

In quantum mechanics, particles are described by wave functions, which describe probability amplitudes. In quantum field theory, particles are described by excitations of quantum fields. What is the ...
3
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1answer
69 views

Linearizing Quantum Operators [duplicate]

Possible Duplicate: Linearizing Quantum Operators I was reading an article on harmonic generation and came across the following way of decomposing the photon field operator. $$ ...
4
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1answer
209 views

Linearizing Quantum Operators

I was reading an article on harmonic generation and came across the following way of decomposing the photon field operator. $$ \hat{A}={\langle}\hat{A}{\rangle}I+ \Delta\hat{a}$$ The right hand side ...
4
votes
4answers
5k views

What is a correct and simple definition of quantum physics?

Is it correct to define Quantum Physics as the study of Physics in sub-atomic scale? Does Quantum Physics studies something else other than sub-atomic phenomena? This may be a very stupid question ...
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2answers
5k views

Speed of a particle in quantum mechanics: phase velocity vs. group velocity

Given that one usually defines two different velocities for a wave, these being the phase velocity and the group velocity, I was asking their meaning for the associated particle in quantum mechanics. ...
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2answers
155 views

Do asymptotically similar potentials yield similar energy levels asymptotically?

Let there be given two Hamiltonians $$H_1~=~ p^{2}+f(x) \qquad \mathrm{and} \qquad H_2~=~ p^{2}+g(x). $$ Let's suppose that for big big $x$, the potentials are asymptotically similar in the sense ...
2
votes
2answers
544 views

separation of variables

I'm a math student who's dabbled a little in physics, and one thing I'm a little confused by is separation of variables. Specifically, consider the following simple example: I have a Hamiltonian $H$ ...
4
votes
4answers
649 views

Unitary Operator as a complex valued function

A book on Quantum Mechanics by Schwinger states, "A unitary operator can be considered to be a complex valued function of a Hermitian operator." Please give a hint on how to prove this assertion.
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2answers
5k views

What is “quantum locking”?

I've always assumed that "quantum locking" was a term invented by the writers of Dr Who, but this video suggests otherwise. What is quantum locking? Is it real?
2
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1answer
435 views

electron hole exchange

If exchange is an interaction between indistinguishable particles, how can there be an exchange interaction between electrons and holes? I see mention of e-h exchange often in the literature.
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3answers
1k views

Relation between unitarity and conservation of probability

In a seminar, I heard that the unitary aspect of representations was important physically, because in quantum mechanics unitarity is closely tied to the conservation of probability. Could someone ...
8
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2answers
6k views

How does quantum trapping with diamagnets work?

I just saw this demonstration by someone from a Tel Aviv University lab. What they achieved there is mind blowing. I myself own a levitron that uses the Hall effect to levitate a magnet, the problem ...
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2answers
2k views

Why does Davisson-Germer experiment confirm electron's wave-particle duality?

First I apologize if my question is trivial and for my poor English. I was wondering why my teacher states that "electron's wave-particle duality is verified if we observe diffraction of the electron ...
2
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4answers
242 views

Are Everettian branchings global or local?

Everett's theory of quantum mechanics is about the wavefunction of the whole universe holistically. If a branching occurs very far away at the Andromeda galaxy, do I also branch? Are branchings global ...
9
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1answer
943 views

Why should bosons be in the adjoint representation of the gauge group?

Is there a deep mathematical reason for why bosons should be in the adjoint representation of the gauge group rather than any other representation?
2
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1answer
207 views

Degeneracy and the Hamiltonian

How many linearly independent eigenfunctions can be associated with one degenerate eigenvalue of the Hamiltonian operator? (Is there a limit since it contains a 2nd order differential operator?) ...
2
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1answer
241 views

Can the time direction of wave function collapse be reversed? [duplicate]

The laws of physics are invariant under CPT transformations reversing time, inverting space and flipping charges. Almost so. The collapse of the wave function is the odd man out. Can the time ...
1
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2answers
726 views

Non-unitarity of wave function collapse

Why the wave function collapse corresponds to a non-unitary quantum operation?
2
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1answer
2k views

Probability current

Conservation of probability: Suppose a wavefunction has ${\partial \mathbb P \over \partial t} = -t f(x,t)$ and ${\partial j \over \partial x} = i f(x,t)$. How does it follow that ${\partial \mathbb P ...
4
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1answer
258 views

Young's double slit

Am I right to think the (general) probability distribution of photon in a double slit experiment at the screen has the form $|\psi|^2 = c e^{\alpha x^2}\cos^2(\beta x)$? (Due to the superposition of ...
4
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1answer
39 views

Connections of iterative solvers for large systems of equation in Physics?

I am trying to find the domains in physics where solving large systems of equations is computationally expensive. The sparse systems are of my particular interest, where the input matrix A is in GBs ...
5
votes
4answers
1k views

How does a state vector be projected onto an eigenspace after measurement

In http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Degenerate_spectra, it is said that If there are multiple eigenstates with the same eigenvalue (called degeneracies),..., The ...
20
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5answers
582 views

direct sum of anyons?

In the topological phase of a fractional quantum Hall fluid, the excitations of the ground state (quasiparticles) are anyons, at least conjecturally. There is then supposed to be a braided fusion ...
2
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1answer
868 views

Superposition of wavefunctions

Suppose you have 2 normalized wavefunctions $\psi_1=Ne^{iax}e^{if(x)}e^{i\omega t}$ and $\psi_2=Ne^{-iax}e^{if(x)}e^{i\omega t}$ defined on $x\in [-x_0,x_0]$ and vanishes for $|x|>x_0$. What then ...
4
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0answers
671 views

Raman Scattering and the Kramers-Heisenberg Formula

Using the words of the wikipedia article Raman Scattering: The Raman effect corresponds, in perturbation theory, to the absorption and subsequent emission of a photon via an intermediate ...