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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What is the difference between realism in locality, and counterfactual definiteness?

I understand the EPR-experiment and the Bell inequalities. I can see how dropping 'locality' solves the issue, and how dropping 'realism' solves the issue (e.g. there are really no hidden variables ...
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77 views

normal ordering from anti normal ordering of creation and anhilation operators

I am working on entanglement of systems in beam splitters. I constantly come across equations of creation and annihilation operator (ladder operators) in anti normal ordering. I want those equations ...
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2answers
830 views

Quantum Mechanics: Creation and Annihilation operators

Is an eigenvector/eigenstate of the creation operator an eigenvector/eigenstate of the annihilation operator too? Why?
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4answers
351 views

Detecting a photon without changing it: Does it break conservation laws?

This is about an article published on ScienceMag: Nondestructive Detection of an Optical Photon. I don't have access to full text, but you can see a brief transcription in this link. Basically, it ...
4
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1answer
246 views

Can general wavefunctions be expressed as kets?

I am confused on bra-ket notation in quantum mechanics. My professor says that a ket is an eigenfunction of some operator. However, for some time now I thought a ket could represent a general ...
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4answers
464 views

Is uncertainty principle a technical difficulty in measurement?

I have searched for an answer to this question on physics SE but I have not seen a question in which it is addressed properly. Please let me know if there is an answer already. My question briefly ...
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192 views

Notation in Quantum Mechanics

When we write equations in QM, in certain places, the wave function is represented as $\psi(x,t)$, which is the wave function in position space, and in some other places, it is written as $\Psi(t)$. ...
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92 views

Decomposition of two particle wavefunction into product of single-particle wavefunctions

Suppose you prepare a two-particle system such that $\Psi(\vec{r}_1,\vec{r}_2, t_0) = \Psi_1(\vec{r}_1, t_0)\Psi_2(\vec{r}_2, t_0)$. So then, initially $\Psi(\vec{r}_1,\vec{r}_2,t_0) - ...
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259 views

Probability of absorption and emission of photons

Suppose you have a single electron in a box, and you shoot a single photon at it. How does one calculate the probability that the photon will be absorbed and the particle excited? Or that the photon ...
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0answers
51 views

Solving for the phase shift of a neutron due to precession in magnetic field

In the famous experiment that was used to prove the sign change of the wave function due to a rotation of 2$\pi$ by Werner et al. It is stated directly that the phase shift of the neutron beam is ...
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1answer
313 views

Explanation for the power of quantum computers

I have seen various explanations for the power of quantum computers: Quantum computers perform operations in parallel universes Quantum computers can use quantum tunneling to reach a global extremum ...
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1answer
71 views

Mean kinetic energy according to the WKB approximation

Show that in the WKB approximation, the mean kinetic energy $T_{n1}$ in a bound state $\psi_n$ in a potential $V(x)$ is given by $\langle T_n \rangle = \frac{1}{2}\left(n+\frac{1}{2}\right) ...
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1answer
169 views

Why are Hermitian operators linked to observables?

In Quantum Mechanics, why is it that a self-adjoint operator is linked to an observable? What makes it measureable? And why isn't a non-Hermitian operator linked to an observable? Also, what type of ...
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2answers
337 views

How does the proof of operator commutativity work with non-continuous operators?

In some books, a proof that if two self-adjoint operators $A$ and $B$ share a common eigenbasis $\{\phi_n\}$, then they commute is given as follows : For any $\phi_n$, $$AB\ \phi_n = a_n\ ...
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546 views

Wave packets and the derivation of Schrodinger's equation

I studied in my class, that a plane progressive wave cannot be used to represent the wave nature of a particle as it is not square integrable. Also, the phase velocity can get above the value of $c$, ...
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107 views

Discord for partially decohered bell state

To illustrate discord and its use, Zurek in his paper on discord (NB pdf) gives example of a partially decohered bell state i.e. $$\rho_{AB}=\frac{1}{2}(|00\rangle\langle 00|+|11\rangle\langle 11|) + ...
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136 views

What is the difference between a one-particle state in the fock space and single particle wave function (in momentum representation)

If I consider one single Dirac electron in momentum representation, I use the wavefunction $u(p)e^{-ipx}$, however if I consider an one-particle state in the Fock space I use $|p\rangle$. Should it ...
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0answers
221 views

Continous and Discrete basis, Multiplication of Density Matrix and Hamiltonian

Suppose I have a wave function $\psi(x)$ in position basis. I can make a density function by simply multiplying $\psi(x)$ and its conjugate $\psi^*(x)$. If I operate the density matrix ...
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1answer
308 views

Probability in Quantum Mechanics: General

How do I find the most probable value of position of a (non-Gaussian) wave function? Is it the same value as the expectation value of the position? And is it true that the most probable value of ...
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1answer
193 views

How can Superconductivity materials levitate permanent magnet?

I have thought that by eddy current. But how eddy current in superconductivity materials can be generated by using permanent magnet?
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1answer
212 views

Could two different bases of a Hilbert space have different cardinality? [duplicate]

Here is a quote from http://en.m.wikipedia.org/wiki/Hilbert_space#Hilbert_dimension (accessed: Nov. 22, 2013) : As a consequence of Zorn's lemma, every Hilbert space admits an orthonormal basis; ...
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1answer
106 views

How are atomic bonds created?

From what I have learned in my chemistry course, Electrons with similar quantum numbers but with opposite spin are attracted to each other. What does this mean when there is a covalent bond being ...
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3answers
357 views

Why not formulate Quantum Mechanics using Lagrangians? [duplicate]

As the title implies, why is it that the most common formalisms we use in quantum mechanics prefer to describe systems in the terms of a Hamiltionian instead of a Lagrangian? Is there some ...
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2answers
414 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec ...
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1answer
209 views

electric potential energy symbol in Schrodinger equation

In my introductory physics class, $V$ is the symbol for electric potential (joules per coulomb) and $U$ is the symbol for electric potential energy (joules). Since the Schrodinger equation is the ...
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5answers
257 views

Why does the universe follow the uncertainty principle?

I have been thinking about this question for quiet a long time but, couldn't make up an answer myself. Usually when someone asks about why a system is the way it is we answer it by saying that it is ...
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44 views

Some question on the definition of flux in the projective construction?

Here I have some confusing points about the definition of flux in the projective construction. For example, consider the same mean-field Hamiltonian in my previous question, and assume the $2\times 2$ ...
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1answer
103 views

Some conceptual questions in BEC

In Bose-Einstein condensate (BEC), people often say there is a well defined macroscopic phase. What exactly the macroscopic phase is? (a phase factor $\mathrm{e} ^{i\phi}$ in a many-body wavefuction?) ...
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1answer
385 views

Eigenvectors of the angular momentum operator $S_x$ [closed]

For a spin of $\frac{1}{2}$ the angular momentum operator can be written as $\vec{S} = \frac{\hbar}{2} \vec{\sigma}$ in matrix form. Find the eigenvalues and eigenvectors of $S_x$ where $\sigma_x = ...
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127 views

Single photon double slit experiment

In the question Double Slit experiment with just one photon or electron, one of the answers says There have been experiments recently where one can detect which the slit the particle went through ...
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1answer
69 views

How does the following commutator for measured observables and this operator relation imply the following relation?

$$ \hat{\Omega}_j{(\tilde{q}_j)}=\Omega_j(\tilde{q}_j-\hat{q}_j) $$ $$ [\hat{q}_j,\hat{q}_l]=ik_{jl} $$ Implies $$ [\hat{q}_j,\hat{\Omega}_l]= ...
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1answer
2k views

Ground State Wavefunction of Two Particles in a Harmonic Oscillator Potential

Question: Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by ...
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1answer
126 views

Product of position eigenvectors at different times

I've been thinking about this, and it might sound like a stupid question, but I can't seem to find an answer anywhere, here goes: Whenever we calculate expecation-values between two position ...
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213 views

Interpreting a Hamiltonian in terms of 'hopping' operators

I am having some trouble interpreting a Hamiltonian in terms of "hopping" operators. The Huckel model for nearest neighbour interaction in graphene is given by $$H=-t\sum_\vec{R}|\vec ...
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2answers
102 views

What happens to the physical properties of electrons after diffraction?

Particle Wave duality shows us that waves and particles are the same thing. Therefore electrons can be viewed as both particles and waves. The wave properties of electrons can be seen in the double ...
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1answer
243 views

Arbitrary Complex Powers of Ladder Operators

Given the following pair of operators $a$ and $a^{\dagger}$ that satisfy the usual bosonic CCR: $$[a,a]=[a^{\dagger},a^{\dagger}] = 0;\ [a,a^{\dagger}] = 1$$ For what values of $\alpha \in\mathbb C$ ...
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2answers
404 views

Some doubts about photons

I am reading Berkeley Physics Course vol. 4 (Quantum Mechanics) , chapter 4 (photons). (1) Section 46: book says: consider a typical photon emitted by the source. It can be regarded as a a wave ...
5
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1answer
327 views

Schrödinger equation for two particles in a 3D box?

This is not a homework question, just a question I have developed to get a better conceptual understanding of the results of the Schrödinger equation. If I had a 3D spherical container or radius R, ...
3
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1answer
2k views

Commutator $[\hat{p},F(\hat{x})]$ of Momentum $\hat{p}$ with a Position dependent function $F(\hat{x})$?

I heard from my GSI that the commutator of momentum with a position dependent quantity is always $-i\hbar$ times the derivative of the position dependent quantity. Can someone point me towards a ...
3
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1answer
138 views

Classical dynamics with Schrodinger equation

What are some interesting classical systems for which the dynamics can be reduced to a many-body Schrodinger equation, at least in some useful regions of phase space, and in particular, with many ...
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3answers
459 views

How to derive the uncertainty relation for a system of arbitrary potential?

I've been trying to understand the derivation of the uncertainty principle for the harmonic oscillator as described here (see pages 100-101). What I don't understand is how the potential for the ...
2
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2answers
64 views

Difference between a central potential that is a point and one that is a sphere?

In quantum physics there is a special case known as a particle in a spherically symmetric potential. I have a problem which is similar to the case of a hydrogen atom in that there is one free ...
3
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1answer
184 views

What does $|x⟩|0⟩$ actually mean in bra-ket notation?

Consider the following quote from Wikipedia's page on Shor's algorithm: Initialize the registers to $Q^{-1/2} \sum_{x=0}^{Q-1} \left|x\right\rangle \left|0\right\rangle$ where $x$ runs ...
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1answer
210 views

A commutation problem in Hubbard model

Does the Hubbard Hamiltonian $$H=-t\sum_{\langle ij\rangle \sigma}c_{i\sigma}^{\dagger}c_{j\sigma}+h.c.+U\sum_{i}n_{i\uparrow}n_{i\downarrow}$$ commute with $\sum_{i}\mathbf{S}_i^2$? where ...
1
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6answers
210 views

Meaning of probability in a multiverse/a many-world interpretation?

Consider me tossing a coin and I got tail as a result on observing it. Then, what would be the result of the 'parallel me' in another universe? If the 'parallel me' gets head as a result then, ...
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63 views

How does linearity of a measurement imply that the commutator of all measured observables are $c$-numbers?

I really don't understand with the linearity conditions I have where this comes from.
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1answer
120 views

Understanding operations of quantum computing advantages

For example, let us examine the case of quantum (discrete) fourier transform. There are $2^N$ samples. How do we initialize these $2^N$ samples into $N$ qubits? I have a hard time understanding this. ...
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How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
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4answers
416 views

When is energy discrete/quantized for a potential well?

Specifically, my question is: Should one expect energy quantization for a particle in the following potential well? More generally, how can one tell whether or not energy should be ...
4
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1answer
201 views

Revisiting the microscopic concept of Touching with some more questions

This question is regarding the amazing answer given by Terry Bollinger at this Phys.SE post. I think this answer is very helpful but i do have some standing questions. He says Once the bonding ...