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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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
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1answer
97 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 ...
10
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2answers
191 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 ...
15
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2answers
119 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
6k 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
59 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
103 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
119 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
269 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
282 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 ...
7
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1answer
556 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
2k 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 ...
35
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3answers
1k 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
1k 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
292 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
600 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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4answers
223 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
294 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. ...
4
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3answers
649 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 ...
18
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1answer
761 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 ...
3
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1answer
336 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
76 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 ...
4
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3answers
743 views

an example of a quantum system for which wigner function transitions to negative values

I want to check my understanding of the Wigner transform and try to understand why and how exactly the probabilistic interpretation drops down as the function goes to zero and then to negative values ...
12
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3answers
214 views

Visualization of 1D spin chain wave fuction

What are the known methods for visualizing quantum states of one-dimensional spin chains? They can be based either on their wave functions or density matrices. My particular interest is in plotting ...
21
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2answers
141 views

Bell polytopes with nontrivial symmetries

Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
15
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4answers
89 views

Why can't noncontextual ontological theories have stronger correlations than commutative theories?

EDIT: I found both answers to my question to be unsatisfactory. But I think this is because the question itself is unsatisfactory, so I reworded it in order to allow a good answer. One take on ...
3
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1answer
400 views

Naïve relativistic schrodinger equation [duplicate]

Possible Duplicate: Why are higher order Lagrangians called 'non-local'? Bjorken and Drell presents the equation: $$i\hbar\frac{d\psi}{dt}=H\psi=\sqrt{p^2 c^2+m^2 ...
3
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2answers
579 views

Trouble with constrained quantization (Dirac bracket)

Consider the following peculiar Lagrangian with two degrees of freedom $q_1$ and $q_2$ $$ L = \dot q_1 q_2 + q_1\dot q_2 -\frac12(q_1^2 + q_2^2) $$ and the goal is to properly quantize it, following ...
4
votes
1answer
572 views

What are independent parameters in Hellmann–Feynman theorem?

A typical example in textbooks about the application of Hellmann–Feynman theorem is calculating $\left\langle\frac{1}{r^2}\right\rangle$ in hydrogen-like atoms. Wikipedia has a nice demonstration of ...
35
votes
2answers
748 views

Physical interpretation of different selfadjoint extensions

Given a symmetric (densely defined) operator in a Hilbert space, there might be quite a lot of selfadjoint extensions to it. This might be the case for a Schrödinger operator with a "bad" potential. ...
16
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3answers
329 views

Quantum computing and quantum control

In 2009, Bernard Chazelle published a famous algorithms paper, "Natural Algorithms," in which he applied computational complexity techniques to a control theory model of bird flocking. Control theory ...
12
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1answer
205 views

Are possible gauge fields in a Lagrangian theory always determined by the structure of the charged degrees of freedom?

An elementary example to explain what I mean. Consider introducing a classical point particle with a Lagrangian $L(\mathbf{q} ,\dot{\mathbf{q}}, t)$. The most general gauge transformation is $L ...
15
votes
4answers
195 views

Is there a Majorana-like representation for singlet states?

I mean the Majorana representation of symmetric states, i.e., states of $n$ qubits invariant under a permutation of the qudits. See, for example, D. Markham, "Entanglement and symmetry in permutation ...
10
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2answers
560 views

Transforming a sum into an integral

I posted this in the mathematical forums. Maybe you will help me. I found an hard article http://prola.aps.org/abstract/PR/v105/i3/p776_1 of yang huang and luttinger. The authors begins with the sum: ...
6
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2answers
1k views

Nonlinear dynamics beneath quantum mechanics?

Yesterday I asked whether the Schroedinger Equation could possibly be nonlinear, after reviewing the answers and material given to me in that thread I feel like my question were adequately answered. ...
7
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6answers
968 views

Could the Schrödinger equation be nonlinear?

Is there any specific reasons why so few consider the possibility that there might be something underlying the Schrödinger equation which is nonlinear? For instance, can't quantum gravity (QG) be ...
6
votes
3answers
2k views

Learn QM algebraic formulations and interpretations

I have a good undergrad knowledge of quantum mechanics, and I'm interesting in reading up more about interpretation and in particular things related to how QM emerges algebraically from some ...
1
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1answer
444 views

Sudden change in the Hamiltonian

Could someone explain what this sentence mean? "If the Hamiltonian changes suddenly by a finite amount, the wavefunction must change continuously in order that the time-dependent Schrodinger equation ...
4
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1answer
2k views

3D Quantum harmonic oscillator

For an isotropic 3D QHO in a potential $$V(x,y,z)={1\over 2}m\omega^2(x^2+y^2+z^2).$$ I can see by independence of the potential in the $x,y,z$ coordinates that the solution to the Schrodinger ...
2
votes
1answer
4k views

Degeneracies of the first excited state

I have a box with $x,y,z$ all ranging from 0 to $l$. It has $V(x)$=0 inside and =$\infty$ outside. By extending the 1D Schrodinger equation, I have that the allowed energy eigenvalues are ...
2
votes
1answer
936 views

Expectation of a commutation relation

Is there any significance to: $\langle[H,\hat{O}]\rangle =0$ (which can easily be shown) where $H$ is the Hamiltonian, $\hat{O}$ is an arbitrary operator? Thanks.
4
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1answer
337 views

Projection of states after measurement

Continuing from the my previous 2-state system problem, I am told that the observable corresponding to the linear operator $\hat{L}$ is measured and we get the +1 state. Then it asks for the ...
21
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3answers
2k views

Why can't quantum teleportation be used to transport information?

Kaku Michio says in an interview that we've teleported photons, cesium atoms and beryllium atoms. Having watched a lot of Kaku as well as way too many astrophysics documentaries in general, I know ...
0
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1answer
437 views

Two-state system problem

Given a 2-state system with (complete set) orthonormal eigenstates $u_1, u_2$ with eigenvalues $E_1, E_2$ respectively, where $E_2>E_1$, and there exists a linear operator $\hat{L}$ with ...
5
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2answers
2k views

What is postselection?

I was reading some questions here. I couldn't understand what it means by postselection. What is postselection? What is its use/significance? Where did it came from?
3
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2answers
675 views

Infinite square well

 1. Given that for an infinite square well problem, $\psi(x,0)=\frac{6}{a^3}x(a-x)$, I can show by Fourier transform that the probability of measuring $E_n$  for $n$ even is 0. But is there a physical ...
6
votes
1answer
3k views

Eigenfunctions v.s. eigenstates

Is there a difference between "eigenfunction" and "eigenstate"? They seem to be used interchangeably in texts, which is confusing. My guess is that an "eigenfunction" has an explicit ...
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2answers
434 views

Inspecting the form of a wavefunction

Just a quick check: If given a time-independent wavefunction of the form $$\psi(x) = e^{ikx}f(x)$$, where $f(x)$ any arbitrary function of $x$ but one can't factor out another $e^{i\alpha x}$, ...
7
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1answer
943 views

Where can a good treatment of the 'sudden' perturbation approximation be found?

Where can a good treatment of the 'sudden' perturbation approximation be found? A lot of quantum mechanics books have very brief discussions of it but I want to see it in some detail and preferably ...
11
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2answers
605 views

Do stationary states with higher energy necessarily have higher position-momentum uncertainty?

For simple potentials like square wells and harmonic oscillators, one can explicitly calculate the product $\Delta x \Delta p$ for stationary states. When you do this, it turns out that higher energy ...