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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Graphene's Tight Binding Hamiltonian

Graphene has two atoms in its primitive unit cell. This makes it intuitive to see that the tight binding Hamiltonian can be constructed as a $ 2 \times 2 $ matrix $H$ acting on a spinor $S$ that ...
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Is the symmetrisation postulate unnecessary according to Landau Lifshitz?

The symmetrisation postulate is known for stating that, in nature, particles have either completely symmetric or completely antisymmetric wave functions. According to these postulate, these states are ...
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BEC in a rotating disc

Goodmorning everybody, I have to run a numerical simulation of a Bose-Einstein condensate on a rotating disc. Now, my problem is that I became suspicious about the equation I'm using, since the final ...
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Why does nonlinearity in quantum mechanics lead to superluminal signaling?

I recently came across two nice papers on the foundations of quantum mechancis, Aaronson 2004 and Hardy 2001. Aaronson makes the statement, which was new to me, that nonlinearity in QM leads to ...
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States versus ensembles in quantum mechanics

In quantum mechanics, we talk about (1) vectors, (2) states, and (3) ensembles (e.g., a beam in a particle accelerator). Suppose we want to translate this into mathematical definitions. If I'd never ...
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Quantum tunelling problem - got a weird imaginary ratio in the end

1. The problem statement, all variables and given/known data Beam of electrons with energy $10eV$ hits the potential step ($8eV$ high and $0.5nm$ wide). How much of the current is transmitted? ...
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How to solve bound states of 2D finite rectangular square well?

I want to solve bound states (in fact only base state is needed) of time-independent Schrodinger equation with a 2D finite rectangular square well \begin{equation}V(x,y)=\cases{0,&$ |x|\le a ...
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2answers
527 views

Is it possible for dark matter to somehow turn into regular matter?

Is it possible for dark matter to create the regular matter that we, the stars, and the galaxies are made of? The reason I'm asking this is because I have a hard time imagining how something can ...
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189 views

Are locality and separability two distinct notions?

Is there any difference between locality and separability in quantum mechanics, or do they mean the same thing? It seems authors do not always agree.
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The Momentum Operator in QM

I've seen the 'derivation' as to why momentum is an operator, but I still don't buy it. Momentum has always been just a product $m{\bf v}$. Why should it now be an operator. Why can't we just multiply ...
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In famous Einsteins Photoelectric effect, Why does intensity of light doesn't raise the kinetic energy of the emitting electrons?

The work function of any metal is no doubt constant for it is related to electromagnetic attraction between electrons and protons. However on increasing the intensity of any light source the kinetic ...
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Moving electron - finding the wavefunction

On our modern physics class my professor did a problem: Write down a wavefunction of an electron which is moving from left to right and has an energy $100\text{ eV}$. At first i said: "Oh i know ...
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Fermi's golden rule and Probabilities in QM

In Fermi's golden rule $$P_{ab}(t)=2\pi t/\hbar \left|\langle\psi_b|V|\psi_a\rangle\right|^2 \delta(E_f-E_i)$$ for transition probability from state $a$ to $b$, how can the probability grow with ...
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QM - calculating expectation value for velocity of an electron

How do we calculate the expectation value for speed? I have heard that we must first calculate the expectaion value for kinetic energy. Someone please explain a bit what options do we have.
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701 views

Polarisation of Light and Atomic Excitation

How does an atomic transition between ground and excited states depend upon the direction of polarisation of incident light?
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568 views

Confusion about wavefunction separability

A wavefunction is inherently a multi-particle function. If you have a container that is perfectly isolated from the external universe (not possible, but just imagine it) and filled with $n$ ...
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Why does a force field leave the momentum operator unchanged in the Schrödinger equation?

The reasoning leading to the Schrödinger equation goes as follows: A plane wave in empty space has the following form: $$\psi = e^{i(kx-\omega t)}$$ Einstein had previously explained the ...
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Wavefunction as a combination of two stationary states - how to find those states?

Lets say we have a particle in a infinite square well which has a wavefunction like this ($A$ is some constant and $d$ is the width of the well): \begin{align} A\left[ \sin \left(\frac{2 \pi ...
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454 views

Dirac Delta Potential and bound/scattered states

Why does the attractive Dirac Delta distribution (function) potential $V = \alpha\delta$(x) (for negative $\alpha$) yield both bound AND scattered states? Is this due to the definition of the Dirac ...
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Bounded and Unbounded (Scattering) States in Quantum Mechanics

I understand that bounded states in quantum mechanics imply that the total energy of the state, $E$, is less than the potential $V_0$ at + or - spatial infinity. Similarly, the scattering state ...
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Finite potential well problem - calculating the ground state

1. The problem statement, all variables and given/known data Electron of is in a 1-D potential well of depth $20eV$ width $d=0.2 nm$ in his ground state $N=1$. What is the energy of the ground ...
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Born's Rule, What is the Reason? [duplicate]

As far as I've read online, there isn't a good explanation for the Born Rule. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives ...
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How to superpose an wavefunction for an infinite potential well / interval - $-d/2 <x<d/2$

I know that two functions which describe the state of a particle in an infinite square (on interval $-d/2<x<d/2$) well are like: \begin{align} \psi_{even}&= ...
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On the atomic level, how is incandescent light structured?

I want to know from the smallest possible originating structures how the light I see generated from heat is made by atoms themselves.
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Orthogonality of the wavefunctions on an subinterval?

Lets say that functions (eigenfunctions) $\psi_0$ and $\psi_1$ are orthogonal on an interval $-d/2 < x < d/2$. Are they also orthogonal on any subinterval inside the interval $-d/2 < x < ...
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398 views

Unitary transformations in mixed discrete-continuous representations

I am having trouble with the unitary transformation of a certain Hamiltonian in the paper Zhai, H. Spin-orbit coupled quantum gases. Int. J. Mod. Phys. B 26 no. 1, 1230001 (2012). arXiv:1110.6798 ...
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Pauli matrices as measurement operators

I am trying to understand a paper on the Bell test experiments. I understand that if we wanted to measure the spin of a spin-1/2 particle in state $\psi$ along the z-axis we would apply the operator ...
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214 views

How do we measure a quantum system properties? (length, mass and time) [closed]

How do we measure a quantum particle properties? (length, mass and time)
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250 views

Should normalisation factor in a QM always be positive?

I have a fairly simple question about a normalisation factor. After normalising a wavefunction for a particle in an infinite square well on an interval $-L/2<x<L/2$ I got a quadratic equation ...
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Doubts about the Aharonov-Bohm effect

In F. Schwabl, Quantum Mechanics p.148 it is explained that if we have a particle in an electromagnetic field given by potentials $\varphi$ and $\mathbf{A}$ with wave function $\psi$, then a gauge ...
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What are physical effects that could be employed to emulate this system?

This is a simple system consisting of a tree of numbers such as ((1 2 (3 4)) (2 6) 1 6) and a rule of application, that states that a tree A applied to B is a copy ...
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2answers
693 views

Linearity of Quantum Mechanics?

The proof of the No-Cloning Theorem states "By the linearity of quantum mechanics, ..." -- Could someone please give me a rough sketch/outline of what this means? Does it have to do with the Hilbert ...
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1answer
609 views

Coupled Oscillators

This is an exercise of my last exam. Since I couldn't find anybody who solved it or knows how to, it would be really nice if somebody could tell me if my thoughts on it go into the right direction. ...
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Quantum physics and separation fallacy

I'm deeply interested in understanding delayed choice eraser experiment. Although I understand the experimental results, the retro causality is causing a big headache. From what I understand, the ...
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WolframAlpha wont reckognize a second derivative inside an integral [closed]

I know that WolframAlpha questions are off topic but as I cannot find a Q&A site for WA I decided to ask here. It should be a piece of cake for you guys as I think it is a fairly simple question. ...
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328 views

Orbital of Hydrogen molecule

does anybody here know an analytical approximation of the bonding hydrogen orbital MOLECULE? I am looking for a good approximation to this orbital, that might be in some textbooks to get an ...
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2answers
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The Energy Eigenvalue of a Wavefunction

I've been reading an introduction to quantum mechanics online, and while constructing the Schrodinger equation for a free particle, the equation $i\hbar \frac{d \Psi}{dt}=\hbar\omega\Psi$ is obtained. ...
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Calculating the expectation value for kinetic energy $\langle E_k \rangle$ for a known wave function

I have a wavefunction ($a=1nm$): $$\psi=Ax\exp\left[\tfrac{-x^2}{2a}\right]$$ for which I already calculated the normalisation factor (in my other topic): $$A = \sqrt{\frac{2}{a\sqrt{\pi a}}} = ...
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876 views

After normalizing a wavefunction I don't know how to calculate probability on an interval (-0.1 + 0.1)

This is quite large homework where I 1st had to normalize the wavefunction $\psi = Axe^{-x^2/2a}$ and I got a constant $A=\sqrt{2/(a\sqrt{\pi a})}$. How do I calculate the probability now for the ...
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4answers
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Does quantum mechanics violate the equivalence principle?

I have a question about equivalence principle in quantum mechanics. Consider a Schroedinger equation under gravitional field $$\left[ - \frac{1}{2m_I} \nabla^2 + m_g \Phi_{\mathrm{grav}} \right]\psi ...
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Adiabatic quantum evolution of single photon or biphoton system

The prerequisite for adiabatic quantum evolution of single photon or biphoton system is as follows. We have to prepare a single photon or biphoton quantum system which has a ground and a higher level ...
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372 views

Two-oscillator system coupled to reservoir

I am implementing the Monte Carlo wave-function approach to dissipation problems. So far, I have simulated the quantum harmonic oscillator coupled to a finite temperature reservoir given in section ...
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159 views

Is there an idealist rather than realist interpretation of QM?

The many-worlds interpretation of QM is a realist explanation as it makes the wave function of the universe real. That is it makes the probabilities of outcomes real outcomes. One could argue that ...
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Uncertainty and wave-trains

My textbook and the following extract from feynman's lectures present the same idea regarding wavetrains and uncertainty in their wavelengths. Why is it that a wavetrain confined to some space has an ...
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3answers
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How can the quantum state of the universe decohere

Decoherence explains how a classical state appears once quantum information in a quantum state leaks out. But presumably that environment has its own quantum state which then leaks out to a larger ...
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521 views

If there is no collapse of the wave-function does this mean that the many worlds interpretation of QM must be wrong?

If as some people suggest, there is no collapse of the wave function (is there a standard name for this position), then must one rule out the many-worlds interpretation of QM?
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Why does the classical equivalent to a quantum computer take so many bits?

A quantum computer with 10 qubits is classically equivalent to $2^{10}$ bits. How is this equivalence worked out? I understand that a single qubit is a vector in a 2-dimensional hilbert space, whose ...
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What happens after the collapse of a wavefunction?

If I have a quantum system which I prepare in a certain state, this state then evolves unitarily via a Hamiltonian. Suppose an observer provokes a collapse of the wave function by a certain ...
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Hermite polynomials for expected value of harmonic oscillator

This was a problem on my final exam that has been really bugging me. Consider the quantum Harmonic oscillator prepared in an energy eigenstate, $\psi_n$(x). Calculate the expectation value of the ...
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Derivation for 7.14 in Atomic Physics by Foot

I was going thru Ch7 of Foot and trying to fill in the gaps. However I got stuck on (7.14). So Foot was working with a two level system with a small perturbation in the Hamiltonian resulted from an ...