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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Matter waves and de Broglie wave length

The wavelength of a particle of momentum p is calculated using De Broglie relation. The de Broglie relation was postulated for what is called a matter waves. Now according to the statistical ...
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Why is Gleason's Theorem not enough to obtain Born Rule in Many Worlds Interpretation?

The Many Worlds interpretation suffer from at least 2 "wounds", the preferred basis issue and perhaps the most notorious probability issue. How do you make sense of probability in a model where ...
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quantum optics of a polarizing beam splitter

I would like to use the Heisenberg picture in quantum field theory to model a polarizing beam splitter. Is there an easy way for someone to show me how the field operators ($a^\dagger_{input1}$, ...
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118 views

Matlab package: graphical calculus for quantum operations including beam splitters and polarizing beam splitters [duplicate]

I need a matlab package that will make my life easier. I have quantum circuits with optical beam splitters, polarizing beam splitters and photodetectors. These circuits are getting very complicated ...
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1answer
90 views

Spatial and polarizing beam splitters in a graphical calculus

Suppose I have four wires, and I tensor product them together $A \otimes B \otimes C \otimes D$ I pass $A \otimes B$ through a spatial beam splitter $Spl: A \otimes B \rightarrow A^\prime \otimes ...
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1answer
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Compatible Observables

My QM book says that when two observables are compatible, then the order in which we carry out measurements is irrelevant. When you carry out a measurement corresponding to an operator $A$, the ...
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2answers
2k views

Why electrons are relativistic in Graphene and non relativistic in vacuum?

If a free region in space has a potential difference of one volt, an electron in this region will acquire kinetic energy of 1 eV. Its speed will be much smaller than the speed of light hence it will ...
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2answers
656 views

The quantum state can be interpreted statistically, again

Now there are two papers The quantum state cannot be interpreted statistically http://arxiv.org/abs/1111.3328 (It was discussed here the consecuences of this "no-go theorem") And this one (two of ...
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3answers
614 views

Can a photon be emitted with a wavelength > 299,792,458 meters, and would this violate c?

Just curious if the possibility exists (not necessarily spontaneously) for a photon with a wavelength greater than the distance component of c to be emitted, and would this inherently violate the ...
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2answers
964 views

Why does iteratively solving the Hartree-Fock equations result in convergence?

[ Cross-posted to the Computational Science Stack Exchange: http://scicomp.stackexchange.com/questions/1297/why-does-iteratively-solving-the-hartree-fock-equations-result-in-convergence ] In the ...
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2answers
418 views

What are some ways to (approximately) symbolically diagonalize Hamiltonian operator?

Specifically the Hamiltonian takes the form of $$\hat H = \frac{\Delta }{2}{\hat \sigma _z} + {\omega _1}\hat a_1^\dagger {\hat a_1} + {\omega _2}\hat a_2^\dagger {\hat a_2} + {g_1}\left( {{{\hat ...
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3answers
801 views

Is photon emission possible without electrons changing energy levels?

Does molecular vibrational transition and consequent emission of infrared radiation involve electrons changing energy level? In wikipedia, about vibronic transitions it says "Most processes leading to ...
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1answer
572 views

Why is the value of spin +/- 1/2?

I understand how spin is defined in analogy with orbital angular momentum. But why must electron spin have magnetic quantum numbers $m_s=\pm \frac{1}{2}$ ? Sure, it has to have two values in ...
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0answers
168 views

Nonablianity of Wilczek Zee Potential

Consider a hamiltonian with degeneracies of energy in parameter space $(R)$.Now the Geometric phase(Wilczek Zee Potential) will acquire a non abelian nature. To prove the non abelian nature of Wilczek ...
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2answers
592 views

What is the Hilbert space of a single electron?

Is it the same as the space of all possible descriptions of a single electron? If not, how do they differ? Please give the mathematical name or specification of this space or these spaces.
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0answers
83 views

Spectrum of a quantum relativistic “distance squared” operator

This question disusses the same concepts as that question (this time in quantum context). Consider a relativistic system in spacetime dimension $D$. Poincare symmetry yields the conserved charges $M$ ...
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0answers
265 views

Symmetries of separable potential

For separable potential, say $x^4+y^4$, its symmetry are degenerate. Is that a generic case to every separable potential? I will explain my question: The potential $x^4+y^4$ has $A_1, B_1, A_2, B_2, ...
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3answers
707 views

Quantum harmonic oscillator

I read somewhere that a quantum field can be thought of as a tiny bowl at every point in space with a ball doing SHM (quantum harmonic oscillator). It was given that the amplitude of this SHM is ...
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1answer
555 views

Vibrational motion of linear diatomic molecule

This question concerns the following exercise from an old exam: The vibrational motion of a linear diatomic molecule can be approximated as simple harmonic motion. A CO molecule has a bond ...
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2answers
230 views

What are the practical applications of decoherence?

Let me clarify this question somewhat. I know decoherence is ubiquitous in nature and explains the emergence of a classical world from quantum physics. My question is really about how a knowledge of ...
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2answers
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Incompatibility Between Relativity and Quantum Mechanics

Why does Gravity distort space and time while the electromagnetic, strong, and weak forces do not? Does this have to do with why Quantum Mechanics and Relativity are incompatible?
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1answer
743 views

Wave function of hydrogen atom including spin of nucleus

How do I write the wave function of hydrogen atom taking into consideration of nucleus spin? For example consider $2S_{\frac{1}{2}}$ state with nucleus spin $I$, then wave function ...
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1answer
174 views

Electron shell bombardment

If you bombard an electron shell with a photon below the critical level to promote the electron to a higher state, will the shell absorb nothing and the photon get deflected with the same amount of ...
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5answers
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How are the Pauli matrices for the electron spin derived?

Could you explain how to derive the Pauli matrices? $$\sigma_1 = \sigma_x = \begin{pmatrix} 0&1 \\ 1&0 \end{pmatrix}\,, \qquad \sigma_2 = \sigma_y = \begin{pmatrix} 0&-i\\ ...
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3answers
718 views

One dimensional Schrödinger equation equation with initial condition, finding the probability of the particle's future position

A particle of mass $m$ moves freely in the interval $[0,a]$ on the $x$ axis. Initially the wave function is: $$f(x)=\frac{1}{\sqrt{3}}\operatorname{sin}\Big( \frac{\pi x}{a} ...
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1answer
158 views

random matrix ensembles from BMN model

My friends working on Thermalization of Black Holes explained solutions to their matrix-valued differential equations (from numerical implementation of the Berenstein-Maldacena-Nastase matrix model) ...
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1answer
341 views

Relativity and Entanglement

Say we have two particles which are entangled so that they have opposite spins. If one is up, the other is down. They are sent off to two spatially separated observers A and B. Both observers can ...
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1answer
90 views

Many body quantum states analyzed as probabilistic sequences

Measurements of consecutive sites in a many body qudit system (e.q. a spin chain) can be interpreted as generating a probabilistic sequence of numbers $X_1 X_2 X_3 \ldots$, where $X_i\in ...
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1answer
693 views

Solution to the Schrodinger equation for periodically time dependent Hamiltonians

I have a Hamiltonian which is time dependent but possesses periodic symmetry: $H(t+t_0)=H(t)$. Is there any clever techniques to exploit this? Edit: In particular, I would like a practical method to ...
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9answers
22k views

Why don't electrons crash into the nuclei they “orbit”?

I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course. In particular, I can't see how a negatively charged electron can stay ...
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1answer
92 views

How are particle simplices associated into complex particles?

Nonfundamental particles are seen as made up of fundamental particles (in whatever specific theory). consider the simple case of 2 simplex particles (subscript 1 and 2) which form a complex particle ...
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2answers
238 views

Expressing a particle's matter wave in terms of its momentum

I'm following Zettili's QM book and on p. 39 the following manipulation is done, Given a localized wave function (called a wave packet), it can be expressed as $$\psi(x,t) = \frac{1}{\sqrt{ 2 \pi}} ...
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1answer
302 views

Infinite quantum well width $L$ to $2L$ adiabatic process

If we change width of the infinite quantum well $L$ to $2L$ slowly enough, how it does change energy levels.
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2answers
478 views

Conceptual puzzles when using Coulomb's potential in solving the hydrogen atom in non relativistic QM

When solving the hydrogen atom in non relativistic quantum mechanics we use Coulomb's potential, $\sim1/r$, to describe the interaction between the proton and the electron. I am worried about two ...
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4answers
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Can Planck's constant be derived from Maxwell's equations?

Can mathematics (including statistics, dynamical systems,...) combined with classical electromagnetism (using only the constants appearing in chargefree Maxwell equations) be used to derive the Planck ...
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1answer
126 views

What is an isoscalar factor?

I need to find a definition for "the isoscalar factors of 3j-symbols for the restriction $SO(n)\supset SO(n-1)$...denoted by brackets with a composite subscript $(n: n-1)$..." They are given as: $$ ...
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3answers
693 views

Hilbert space and Lie algebra in quantum mechanics

We are looking for a publication or website that explains the Standard Model in terms of Hilbert space and Lie algebra. We are reading Debnath's Introduction to Hilbert Spaces and Applications and ...
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5answers
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What is the connection between Poisson brackets and commutators?

The Poisson bracket is defined as: $$\{f,g\}_{PB} ~:=~ \sum_{i=1}^{N} \left[ \frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} - \frac{\partial f}{\partial p_{i}} \frac{\partial ...
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3answers
2k views

Smoothness constraint of wave function

Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't ...
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3answers
270 views

POVMs that do not require enlargement of the Hilbert space

The usual justification for regarding POVMs as fundamental measurements is via Neumark's theorem, i.e., by showing that they can always be realized by a projective measurement in a larger Hilbert ...
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1answer
189 views

Solutions to SHMO equation in Feynman's Thesis

I'm reading Feynman's Thesis, and have some background in math and physics, but I'm not sure where Feynman gets his solution to his harmonic oscillator equation. He gives three different ...
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2answers
1k views

Double-slit experiment simulated with water waves?

We all know the explanation videos and other material using the water waves analogy to illustrate the propagation of electrons or photons and the interference patterns measured in the the single-slit ...
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2answers
999 views

Can cellular automata be reconcilied with quantum mechanics?

CAs are deterministic representations of the universe, which, according to the Bell's inequality are not entirely accurate. Cells interact "locally" (only with the closest neighbours), while quantum ...
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1answer
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How to calculate time evolution of a wave function in an 1D infinite square well potential?

A particle in an infinite square well has an initial wavefunction $$\psi (x,0) ~=~ Ax(a-x) \qquad \mathrm{for}\qquad 0\leq x\leq a.$$ Now the question is to calculate $\psi (x,t)$. I have ...
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5answers
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Why is Mendel Sachs's work not taken seriously? Or is it? [closed]

Back in college I remember coming across a few books in the physics library by Mendel Sachs. Examples are: General Relativity and Matter Quantum Mechanics and Gravity Quantum Mechanics from General ...
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4answers
825 views

How can indeterminacy in quantum mechanics be derived from lack of ability to observe a cause?

I don't get this part of quantum mechanics. I get the part that you can't observe particles and not affect their behavior because you are shooting photons to them while you are observing them, but ...
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0answers
321 views

In Scully and Druhl delayed choice quantum eraser experiment, are there limits to the lengths of the delay?

I'm in humanities, not physics, so please bear with me. I am trying to understand this experiment and have a few unanswered questions. I have read the other posts on this site that discuss the ...
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115 views

Derivation of Brillouin-Wigner theory for coupled subpaces

I recall faintly from my quantum theory lecture that there was a really neat way to derive Brillouin-Wigner perturbation theory for the special case of two coupled subspaces that involved a geometric ...
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2answers
155 views

Does an interaction of entangled particles with each-other cause decoherence?

I'll apologize in advance if this is not an appropriate place for my question. My background is not in physics, and my understanding of quantum mechanics is extremely rudimentary at best, so I hope ...
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2answers
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Can the quartic oscillator Hamiltonian be made quadratic?

I'm interested in turning a quadratic + quartic oscillator Hamiltonian, $$H = \frac{p^{2}}{2m} +\frac{kx^{2}}{2} + \lambda x^{4},$$ into a purely quadratic problem. One of the simplest things I can ...