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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331 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 ...
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1answer
284 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 ...
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1answer
154 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 ...
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1answer
201 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?
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2answers
207 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
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2answers
263 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 ...
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1answer
531 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
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3answers
250 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 ...
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1answer
149 views

Heuristic argument for the temeprature dependence of specific heat in the “low” temperature regimes

Here by "low temperature" I meant it in the scale of the characteristic $\hbar \omega$ of the system. One can calculate and show that in the low temperature regime $C_V$ of phonons goes like $T^3$ ...
3
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2answers
1k views

parallel/anti-parallel vs. triplet/singlet description of two spins

If we consider two spins, we can think of the spins as being either parallel (up|up or down|down)or anti-parallel (up|down or down|up). Or we can think of them as being in the triplet or singlet ...
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4answers
1k views

In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?

A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. Is there a one to one correspondence between the potential and its spectrum? If the ...
4
votes
1answer
177 views

Products of Gaussian stochastic process variables

In the classic experimental physics text "Statistical Theory of Signal Detection" by Carl. W. Helstrom, Chapter II, section 4 concerns Gaussian Stochastic Processes. Such a process is observed at ...
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1answer
480 views

Theory of Complex Spectra, Applying Slater-Condon Rules

C.W. Ufford and G.H. Shortley in Physical Review 1932, Vol. 42, pg. 167, separate the two $^2$D's of $d^3$. On page 173 (pg 7 of the PDF) of this article they determine the matrix of the ...
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1answer
419 views

How to prepare a desired quantum state?

Given a quantum state function, we can Fourier expand it in terms of stationary states of the Hamiltonian. So if we want to build that same quantum state approximately all we need to do is to ...
0
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1answer
840 views

Value of Ramanujan Summation In Quantum Mechanics

In mathematics, sum of all natural number is infinity. but Ramanujan suggests whole new definition of summation. "The sum of $n$ is $-1/12$" what so called Ramanujan Summation. First he find the ...
13
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1answer
526 views

How come random matrices can predict energy spectra of heavy atoms?

Some of the applications of random matrices is to find the spectra of heavy atoms in nuclear physics which are usually difficult to find otherwise. How can starting from randomness of some kind, ...
7
votes
3answers
734 views

What is a basis for the Hilbert space of a 1-D scattering state?

Suppose I have a massive particle in non-relativistic quantum mechanics. Its wavefunction can be written in the position basis as $$\vert \Psi \rangle = \Psi_x(x,t)$$ or in the momentum basis as ...
5
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2answers
291 views

Tracking photon color in Bell experiments

In parametric down-conversion, it is said that a driving photon is converted into two entangled photons whose frequencies add up to the driving frequency. Yet in discussions about entanglement ...
4
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1answer
565 views

Physical significane and context in which Dirac introduced the Dirac Delta function

I'd like to know the exact context in which Paul Dirac introduced the Dirac delta function. What was the physical significance of the Dirac delta function when he first used it in Physics ?
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7answers
1k views

The philosophy behind the mathematics of quantum mechanics

My field of study is computer science, and I recently had some readings on quantum physics and computation. This is surely a basic question for the physics researcher, but the answer helps me a lot ...
4
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2answers
933 views

Radial Schrodinger equation with inverse power law potential

Recently I read a paper about solving radial Schrodinger equation with inverse power law potential. Consider the radial Schrodinger equation(simply set $\mu=\hbar=1$): ...
3
votes
5answers
590 views

Trying to understand the EPR paradox

So I keep reading all these articles on the EPR paradox, and I follow them pretty easily right up until it gets to the most important matter. Assuming you are trying to measure x and y spin, ...
3
votes
3answers
909 views

Why is the Ritz combination principle incompatible with Classical Mechanics?

This is a quote from Dirac's Principles of Quantum Mechanics: "(...) if an atomic system has its equilibrium disturbed in any way and is then left alone, it will be set in oscillation and the ...
10
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2answers
974 views

Schrodinger equation in spherical coordinates

I read a paper on solving Schrodinger equation with central potential, and I wonder how the author get the equation(2) below. Full text. In Griffiths's book, it reads ...
7
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2answers
3k views

Solving one dimensional Schrodinger equation with finite difference method

Consider the one-dimensional Schrodinger equation $$-\frac{1}{2}D^2 \psi(x)+V(x)\psi(x)=E\psi(x)$$ where $D^2=\dfrac{d^2}{dx^2},V(x)=-\dfrac{1}{|x|}$. I want to calculate the ground state ...
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3answers
246 views

Hydrogen transition and photon behavior

consider a transition for an electron in the Hydrogen atom from the ground state to the 1st excited state. Let's say this transition occurs through absorption of a photon of exactly the energy ...
3
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1answer
316 views

SO(3) x SU(2) Symmetry of the Hamiltonian

I have a question converning multiplets when describing atoms. Let $H=\sum\limits_{k=1}^{N} (p_{k}^2 - \frac{Z}{|x_{k}|} + \sum\limits_{i<k}^{1..N} \frac{1}{|x_{i} - x_{k}|}$ be a (self-adjoint) ...
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1answer
443 views

Heisenberg's Uncertainty Forms

Can Heisenberg's Uncertainty principle be rewritten in terms of energy density writing $$\Delta E \Delta T \geqslant \hbar/2$$ in factors of energy density $\Delta \sigma \text{ }= \frac{3\Delta ...
4
votes
2answers
313 views

Mixed state after measurement

I'm looking at Section 2.4.1 of Nielsen and Chuang's Quantum Computation and Quantum Information were they derive the density operator versions of the evolution and measurement postulates of quantum ...
4
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2answers
1k views

On numerically solving the Schrödinger equation

I just read a paper 'A pocket calculator determination of energy eigenvalues' by J Killingbeck (1979). Link: http://iopscience.iop.org/0305-4470/10/6/001 I have some questions about section 2. Why ...
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6answers
1k views

Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
3
votes
2answers
2k views

Quantum momentum (De Broglie)

The de broglie hypothesis suggests a particle can be associated with a wave of momentum $p = \hbar k$ my question is the following: how does one arrive at this concept of the momentum of a wave? I ...
4
votes
3answers
65 views

Can the Hanbury-Brown and Twiss effect be used to measure the size of composite objects like galaxies?

I know that the Hanbury-Brown and Twiss effect can be used to measure the size of stars. Can it also be used to measure the size of galaxies?
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2answers
502 views

Essential background for QFT study

The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations: $$\frac{d\sigma}{d\Omega} = ...
3
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1answer
205 views

Does decoherence single out a preferred frame?

Environmentally induced decoherence makes wave function collapse unnecessary. But the environment, usually taken to be some heat bath, introduces a preferred frame. (That in which the total (spatial) ...
5
votes
2answers
306 views

Two paths having the same phase in the path integral approach

In the path integral approach to Quantum Mechanics, can two distinctly different paths of the possible infinite paths have the same phase, i.e can there be a bimodal distribution of the phases ...
2
votes
2answers
508 views

Operator relation involving the logarithm of an operator?

Dirac gives the relation: $\exp(iaq)f(q,p) = f(q, p - a\hbar)\exp(iaq)$ where $\hbar$ is Planck's constant. Can anybody give me the corresponding relation when the $\exp$ function is a $\ln$?
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4answers
217 views

Quantum dots on the nuclear scale!

Quantum dots are quantum systems that are confined by definition on the nano scale. Why didn't people study similar systems on a much smaller scale, something as small as the dimension of the nucleus? ...
2
votes
1answer
517 views

Atomic Transitions - Dipole Approximation

my question concerns the interaction of light and matter in a semi-classical approach. (Quantized Atoms, Classical Fields) In the Coulomb gauge (div A = 0 , $\phi$=0) we have $E = ...
9
votes
2answers
1k views

Poincare group vs Galilean group

One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
3
votes
1answer
238 views

Coincidence detectors in Bell tests: How close is close enough?

When is a coincidence a coincidence? We know that to identify entangled photons, the electronics is set to look for simultaneous clicks at opposite detectors. The size of the window is to some degree ...
4
votes
1answer
399 views

Commutation of operators in quantum theory

I have always written the commutation rules of quantum theory as , $[q,p] = i\hbar\delta _{ij}$ But seems that some people write this as, $[q^i,v_j]= \frac{i\hbar}{M}\delta^i _{j}$ (..this is ...
3
votes
3answers
720 views

Time in special relativity and quantum mechanics

The time is treated differently in special relativity and quantum mechanics. What is the exact difference and why relativistic quantum mechanics (Dirac equation etc.) works?
11
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7answers
1k views

Quantum entanglement vs classical analogy

Consider that we have two balls, one white and one black, and two distant observers A and B with closed eyes. We give the first ball to the observer A and the second ball to the observer B. The ...
2
votes
1answer
556 views

About the delta potential well

If a particle in a delta potential well has negative energy, why the particle will be bound in the well? And if it has positive well, why it is free to move in either half-space: x < 0 or x > 0? I ...
2
votes
5answers
677 views

Radio waves within an atom

What effect does the quantum world have on radio waves? For example, if I could shrink myself down and stand on the nucleus (or even smaller sub atomic particles making up the nucleus) with a device ...
12
votes
1answer
2k views

Solving Schrödinger's equation with Crank-Nicolson method

I am trying to numerically solve Schrödinger's equation with Cayley's expansion ($\hbar=1$) $$\psi(x,t+\Delta t)=e^{-i H\Delta t}\psi(x,t)\approx\frac{1-\frac{1}{2}i H\Delta t}{1+\frac{1}{2}i H\Delta ...
3
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1answer
1k views

What is the Jost function in scattering theory?

What is the Jost function in scattering theory? Is it an operator or some kind of determinant? How is it obtained?
3
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1answer
320 views

Stern-Gerlach-Experiment with j=1 atoms?

Suppose you do a Stern-Gerlach experiment with atoms in a $j=1$ state. There would be three separate beams ($m_j = -1, 0, 1$) coming out of the apperatus. But what would be the relative distribution ...
4
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3answers
569 views

Defining Measurement in Quantum Mechanics

I should begin by saying that I am a total newbie when it comes to Quantum Mechanics. Therefore my question might sound metaphysical to people who know their stuff. So please forgive. What I am ...