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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16
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2answers
202 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 ...
-1
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1answer
131 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
553 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
388 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
votes
1answer
190 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
votes
1answer
658 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
votes
3answers
510 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 ...
5
votes
4answers
1k 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
votes
1answer
65 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
votes
1answer
205 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
2k 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 ...
3
votes
2answers
3k 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. ...
5
votes
2answers
147 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
407 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
548 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.
2
votes
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
votes
1answer
324 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.
7
votes
3answers
887 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
votes
2answers
5k 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 ...
1
vote
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
votes
4answers
238 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 ...
7
votes
1answer
704 views

Adjoint representations and bosons

Is there a deep mathematical reason why bosons should be in the adjoint representation of the gauge group rather than any other representation?
2
votes
1answer
194 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
votes
0answers
188 views

Can the time direction of wave function collapse be reversed?

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
vote
2answers
530 views

Non-unitarity of wave function collapse

Why the wave function collapse corresponds to a non-unitary quantum operation?
2
votes
1answer
1k 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
votes
1answer
245 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
votes
1answer
38 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
953 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 ...
17
votes
5answers
445 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
votes
1answer
662 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 ...
3
votes
0answers
509 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 ...
1
vote
3answers
231 views

observing Quantum Mechanics

When you observe or measure a process in classical physics it almost never really alters the experiment. For example, if you have an Carnot engine and measure the volume and pressure of a gas in some ...
5
votes
2answers
804 views

Energy operator

Does the Hamiltonian always translate to the energy of a system? What about in QM? So by the Schrodinger equation, is it true then that $i\hbar{\partial\over\partial t}|\psi\rangle=H|\psi\rangle$ ...
2
votes
2answers
743 views

Does Hestenes Zitterbewegung Explain why complex numbers appear in QM?

This question may fit better in the discussion of "Why Complex variables are required by QM?", but it also relates to the extent to which arguments by Hestenes are accepted in mainstream physics and ...
2
votes
1answer
514 views

Simple rotation of an atomic orbital wavefunction

We know that an atomic orbital wavefunction may be written in terms of polar coordinates, $$\psi (r, \theta, \phi) = R(r) A(\theta, \phi)$$ where $R(r)$ is the radial component and $A(\theta, \phi)$ ...
26
votes
11answers
2k views

Negative probabilities in quantum physics

Negative probabilities are naturally found in the Wigner function (both the original one and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
5
votes
1answer
877 views

How can we have spinless fermions?

I've read that the Jordan-Wigner transformation changes qubits into spinless fermions. What, exactly, are spinless fermions? I'm guessing it doesn't mean spin zero which would be a boson, so what does ...
17
votes
6answers
562 views

Is there a theorem that says that QFT reduces to QM in a suitable limit? A theorem similar to Ehrenfest's theorem?

Is there a theorem that says that QFT reduces to QM in a suitable limit? Of course, it should be, as QFT is relativisitc quantum mechanics. But, is there a more manifest one? such as Ehrenfest's ...
2
votes
2answers
2k views

When can I use Wick's theorem?

Wick's theorem means that for fermions, a four point correlation function (for example) can be written in terms of two point correlation functions: \begin{equation} \langle b_l^\dagger b_l ...
2
votes
5answers
236 views

Open quantum systems and measuring devices

The Copenhagen interpretation by Niels Bohr insists that quantum systems do not exist independently of the measuring apparatus but only comes into being by the process of measurement itself. It is ...
1
vote
3answers
819 views

What are specific arguments against the ensemble interpretation (as promoted by L. Ballentine)?

Leslie Ballentine develops in QM: A Modern Development an interpretation based on the ensemble interpretation, and responds to most criticisms. My question: what criticisms still exist against this ...
22
votes
0answers
464 views

Orbits of maximally entangled mixed states

It is well known (Please, see for example Geometry of quantum states by Bengtsson and Życzkowski ) that the set of $N-$dimensional density matrices is stratified by the adjoint action of $U(N)$, where ...
11
votes
1answer
87 views

Principle behind fidelity balance in quantum cloning

If we do optimal state estimation on an unknown qubit, we can recreate a state with fidelity $F_c=2/3$ with respect to the original. Let us define the "quantum information content" $I_q=1-2/3=1/3$ as ...
9
votes
1answer
107 views

Quasiparticles in Bohmian mechanics

My questions are about de Broglie-Bohm "pilot wave" interpretation of quantum mechanics (a.k.a. Bohmian mechanics). Do quasiparticles have any meaning in Bohmian mechanics, or not? Specifically, is ...
14
votes
2answers
88 views

Counting complete sets of mutually unbiased bases composed of stabilizer states

Consider $N$ qubits. There are many complete sets of $2^N+1$ mutually unbiased bases formed exclusively of stabilizer states. How many? Each complete set can be constructed as follows: partition the ...
2
votes
5answers
3k views

Is it true that quantum mechanics technically allows anything to happen?

Maybe this is a silly question (I think it is), but it's a question I'm arguing with some of my friends for a long time. The ultimate question is: Is everything (in our Universe) possible ? I've ...
8
votes
1answer
45 views

Sub and super multiplicativity of norms for understanding non-locality

In relation to various problems in understanding entanglement and non-locality, I have come across the following mathematical problem. It is most concise by far to state in its most mathematical form ...
11
votes
1answer
85 views

Stabilizer formalism for symmetric spin-states?

This question developed out of conversation between myself and Joe Fitzsimons. Is there a succinct stabilizer representation for symmetric states, on systems of n spin-1/2 or (more generally) n higher ...
11
votes
1answer
106 views

Metric interpretation of self-adjoint extensions?

I am wondering if beyond physical interpretation, the one dimensional contact interactions (self-adjoint extensions of the the free Hamiltonian when defined everywhere except at the origin) have a ...