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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152 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
94 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
406 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
votes
2answers
619 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
598 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
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2answers
783 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
338 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
207 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
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4answers
209 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
569 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: ...
7
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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. ...
10
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4answers
1k 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
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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
458 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
votes
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
1k 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
351 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
votes
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
448 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
3k 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
687 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
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1answer
4k 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 ...
1
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2answers
457 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
votes
1answer
1k 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
639 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 ...
5
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1answer
276 views

Nomenclature of radial solutions to the Schrodinger Equation

For the free particle with quantum number $l=0$, the regular solution to the radial Schrodinger equation is $R_0 (\rho)=\frac{\sin{\rho}}{\rho}$ while the irregular solution is $R_0 ...
3
votes
1answer
154 views

What is it that undulates in a particle?

When there is a wave, something is undulating. In the example of a rope, the rope is what undulates. In the case of a ripple on a pond, the water is undulating, and when a sound wave propagates, the ...
3
votes
1answer
282 views

under what conditions happen the anti-Zeno effect?

As you might know, the Zeno effect is intuitively expressed as what happens when a system is measured in intervals smaller than the half life of the state it is currently on. As a consequence, the ...
3
votes
2answers
449 views

When is many-body perturbation theory valid?

I'm calculating expectation values (thermal, time-independent) using many-body perturbation theory, but I'm unsure how to work out what values the parameter I'm expanding the perturbation series in ...
5
votes
1answer
596 views

Simultaneously commuting set

How does one determine the members of an simultaneously commuting set (of operators)? For example, I have read that for orbital angular momentum, the set is {$H,L^2,L_z$}. How does one know that these ...
21
votes
3answers
4k views

What's wrong with this derivation that $i\hbar = 0$?

Let $\hat{x} = x$ and $\hat{p} = -i \hbar \frac {\partial} {\partial x}$ be the position and momentum operators, respectively, and $|\psi_p\rangle$ be the eigenfunction of $\hat{p}$ and therefore ...
0
votes
1answer
94 views

References for the source and application of bonding-antibonding splitting on electronic structure?

I am currently doing research on semiconductor materials, so I need a very strong background in band theory to understand the literature. I am currently trying to understand the relationship between ...
3
votes
2answers
266 views

Quantum Fluctuations as a model for the Big Bang?

I have quite often heard (and even used) the idea that quantum fluctuations are a way to explain the whole "something from nothing" intuitive leap. I am about to give a talk at a local school on ...
0
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2answers
1k views

Plotting a wave function that represents a particle

The problem is this: A particle is represented by the wave function $\psi = e^{-(x-x_{0})^2/2\alpha}\sin kx$. Plot the wave function $\psi$ and the probability distribution $|\psi(x)|^2$. This ...
1
vote
2answers
401 views

Schematic expression of the Schrodinger equation

it would be great if someone could help me understand the following quote regarding wavefunctions :) "$$\psi(x)=\sum_n C_nu_n(x)+\int dE C(E)u_E(x)$$ The expression is schematic because we have ...
15
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3answers
10k views

Definite Parity of Solutions to a Schrödinger Equation with even Potential?

I am reading up on the Schrödinger equation and I quote: Because the potential is symmetric under $x\to-x$, we expect that there will be solutions of definite parity. Could someone kindly ...
2
votes
1answer
508 views

Spin up, spin down and superposition

I'm just starting to study quantum mechanics. Please explain the error in this thinking: You set up decay of two $\pi$ mesons and get $2\mathrm{e}^-$ on Mars and $2\mathrm{e}^+$ on Earth. On Earth ...
3
votes
0answers
199 views

Matter-wave interference from free falling cold atoms

and another exam question, this is about current research: Interference of matter waves has been studied using ultra-cold atoms. The phase of a matter wave for free-falling cold-atoms at time $t$ ...
8
votes
3answers
544 views

How does the quantum path integral relate to the quantization of energy?

So, the quantum path integral is a generalization of the classical principle of least action- but here we know that all paths contribute something finite to the probability density. What confuses me ...
3
votes
2answers
493 views

The quantized energy level E depends on which power of n?

A particle in one dimension moves under the influence of a potential $V(x)= ax^6$, where $a$ is a real constant. For large $n$, what is the form of the dependence of the energy $E$ on $n$?
5
votes
1answer
223 views

Is Tsirelson's Bound the only constraint on these quantum correlations?

Alice and Bob are each in possession of one half of a maximally entangled pair of particles. Alice can make either of two observations, $A_1$ or $A_2$. Bob can make either of two observations, $B_1$ ...
2
votes
7answers
372 views

Book request for an abstract treatment of QM without using any particle formalism

I am an electronics and communication engineer, specializing in signal processing. I have some touch with the mathematics concerning communication systems and also with signal processing. I want to ...
1
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1answer
373 views

“Classical” limit of Quantum Hall Effect

Imagine a partially filled $\nu=1$ state of the integer quantum Hall effect (IQHE). One way to think about it is to imagine a gas of electrons where each particle is locked to the lowest quantum state ...
0
votes
1answer
202 views

About the energy with the repulsive potential

Consider the reduced radial Schrodinger equation: $$-\frac{1}{2}\frac{\text{d}^2}{\text{d}r^2}\phi(r)+V(r)\phi(r)=E\phi(r).$$ We try to find a bound state (i.e. $\phi(0)=\phi(+\infty)=0$). Here ...
5
votes
1answer
223 views

What is the energy functional for $\nu=5/2$ Moore-Read state?

I am trying to do some Monte Carlo simulations for Pfaffian state from Fractional Quantum Hall effect. I am wondering what is the energy functional for $\nu=5/2$ Moore-Read state?
2
votes
2answers
245 views

Introducing emf of a chemical cell as a hint towards quantum mechanics

Today I had a discussion with a colleague who teaches electricity and magnetism to 2nd year undergraduate physics students. He is seeking the best way to explain how is the emf generated inside a ...
5
votes
2answers
289 views

What is the basic postulate on which QM rests

What is the basic postulate on which QM rests. Is it that the position of a particle can only be described only in the probabilistic sense given by the state function $\psi(r)$ ? We can even go ahead ...
7
votes
1answer
590 views

Is Bose-Einstein condensate a good example of a classical massive boson field?

Physically, we know that a BEC has formed if a macroscopic number of bosons occupy a single quantum state. The wave-function $\Psi(x)$ of the latter, normalized to the total number of condensed atoms ...
5
votes
3answers
288 views

Why do Bell tests give perfect correlations?

Suppose some decay process emits 2 electrons in opposite directions, and their spin is measured by a Stern-Gerlach type device in a particular direction, say Sz. The books say that if 2 detectors have ...