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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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?
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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.
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3answers
886 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
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 ...
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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 ...
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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 ...
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1answer
702 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?
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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?) ...
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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 ...
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2answers
529 views

Non-unitarity of wave function collapse

Why the wave function collapse corresponds to a non-unitary quantum operation?
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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
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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 ...
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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 ...
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4answers
950 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
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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
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1answer
656 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 ...
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0answers
504 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 ...
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3answers
230 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 ...
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2answers
797 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 $i\hbar{\partial\over\partial t}|\psi\rangle=H|\psi\rangle$ ...
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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
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1answer
512 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 $A(\theta, \phi)$ ...
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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
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1answer
874 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 ...
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6answers
560 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 ...
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2answers
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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 ...
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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 ...
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818 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 ...
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463 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 ...
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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 ...
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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 ...
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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 ...
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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
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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
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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
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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 ...
21
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5answers
172 views

Which symmetric pure qudit states can be reached within local operations?

There are two pure symmetric states $|\psi\rangle$ and $|\phi\rangle$ of $n$ qudits. Is there any known set of invariants $\{I_i:i\in\{1,\ldots,k\}\}$ which is equal for both states iff ...
3
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3answers
260 views

Dirac paper quoted at Wikipedia

From Wikipedia's http://en.wikipedia.org/wiki/Uncertainty_principle: In 1936 Dirac offered a precise definition and derivation of the time-energy uncertainty relation in a relativistic quantum ...
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1answer
457 views

Fundamental particles with spin > 1

I am in undergraduate quantum mechanics, and the TA made an off-hand comment that currently no one knows how to describe fundamental particles with spin > 1 without supersymmetry. I was curious and ...
2
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1answer
848 views

Is traveling at the speed of light the same thing as teleportation?

If I were on one side of the room and moved at the speed of light to the other side of the room, to an observer it would appear that I teleported. If time stops at that speed, it would be ...
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3answers
758 views

What is the use of a Universal-NOT gate?

The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single ...
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1answer
949 views

Radial Schrödinger equation

I found a problem that says: Show by direct substitution that $R_{10}$ is a solution of Schrödinger's radial equation. AFAIK Schrödinger's radial equation is ...
7
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1answer
221 views

How can tunneling be one-way?

I was recently at a lecture given by Dr. Harry Gray, a biophysical chemist, where he talked about how proteins (specifically those involved in photosynthesis) are able to use various phenomena, like ...
4
votes
1answer
452 views

How does thermal broadening of the Fermi Function cause electron coherence loss?

Generally, there are two ways for electrons to lose their wave-like properties in a solid material. One is by way of collisions that cause changes in the energy and momentum of the electron. The other ...
15
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3answers
168 views

Information Retrieval

This question is motivated by the issue of information retrieval from black holes, but it is essentially a question about quantum information. It is widely believed (in certain circles) that the ...
2
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1answer
224 views

weight function and the metric

The weight function comes from Dirac's book, PRINCIPLES OF QUANTUM MECHANICS. On page 66,he says that sometimes it is more convenient not to normalise the eigenvectors, i.e. ...
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3answers
391 views

Stochastic processes and wavefunction collapse

Some time ago I had an idea that, as the unitary evolution of the wavefunction is described by a deterministic equation (PDE, simply), could be the collapse of it be described by some kind of a ...
17
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1answer
605 views

What is the current state of research into $v$-representability?

In their proof, Hohenberg and Kohn (Phys Rev 136 (1964) B864) established that the ground state density, $\rho_\text{gs}$, uniquely determines the Hamiltonian. This had the effect of establishing an ...
2
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1answer
277 views

Spontaneous emission and induced radiation

In Einstein A., Zur Quantentheorie der Strahlung, Phys.ZS., 18, 121-137 (1917) spontaneous emission is considered to occur together with induced radiation so that one can write the following condition ...
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1answer
66 views

Minimum criteria for quantum state dissolution

What are the minimum conditions required to cause the colapse of the quantum state ? Or, what forces/equations determine when an object (for instance an electron) is forced out of its quantum state in ...