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 quantum-field-...

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Information bearing degrees of freedom of a quantum simple harmonic oscillator

I am trying to make sense of arXiv:physics/0210005. I am confused with the concept of information bearing degrees of freedom of a system mentioned at the very beginning. To verify the arguments of the ...
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1answer
661 views

Conservation of Angular momentum in the dipole selection rules

If the total angular momentum J of an atom is not changing during a dipole transition, where does the angular momentum for the photon come from?
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107 views

Do particles travel backward and forward in time? [duplicate]

All these classical ideas are pointless and obsolete today, because in quantum mechanics, the particles are completely different objects, defined by quantum motion of fields, not by the location of ...
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1answer
234 views

Why should multiple versions of a weak measurement preclude it from being a measurement of intrinsic properties of some system

I've been trying to understand Stephen Parrott's criticisms of weak measurement, outlined most concisely here: http://arxiv.org/abs/0909.0295 One of his major criticisms is that weak measurement is ...
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1answer
128 views

Landauer's principle vs Wien's displacement law

Can we argue based on Landauer's principle that if one bit information is changed inside a blackbody, the total radiated energy should be at least or in order of kTln2? If it is so, can we also argue ...
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97 views

Landauer's principle vs Rayleigh–Jeans law

Can we argue based on Landauer's principle that if one bit information is changed inside a blackbody, the total radiated energy should be at least or in order of $kTln2$? If it is so, can we also ...
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0answers
311 views

2D quantum well energy spectrum (analytical vs numerical)

I am trying to understand the energy spectrum difference between the analytical and the approximated solution for a quantum well. The particle is inside a box with domain $\Omega=(0,0)$X$(1,1)$. For ...
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2answers
103 views

N-electron system ground state

The Hamiltonian is given as $H=-\frac{\hbar^2}{2 m_e r^2}\displaystyle\sum_{n=1}^N \dfrac{\partial^2}{\partial \theta_n^2}$ In the first part we show that the $\psi_k=\frac{1}{\sqrt{2\pi}}\exp(i k \...
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1answer
117 views

2 following gates, inverse circuit

I have a circuit that has 4 wires and 2 following each other Toffoli gates. The first Toffoli gate occupies 3 wires from above, the following Toffoli gate occupies 3 wires from below. What will look ...
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0answers
126 views

Counterexamples in quantum theory [closed]

I'm looking for counterexamples in quantum theory, in the spirit of books like Counterexamples in topology and Counterexamples in analysis. A practically identical post, but for PDEs, can be found ...
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1answer
189 views

Experimental perspective in understanding the Heisenberg Uncertainty Principle

I need to confirm whether or not I understand Heisenberg Uncertainty Principle. So the crucial thing is that you need an "ensemble" of measurements: $$\delta x \delta p \ge \frac{\hbar}{2}.$$ If I ...
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0answers
137 views

How large must the Quantum teleportation fidelity have to be in order for it to be useful?

This question relates and stems from my original question. Please read this one and the comments before answering this question. Quantum Teleportation Fidelity I know that for discrete variables ...
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Quantum Mechanics: Show that the expectation value of angular momentum does not change with time

The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$. Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that ...
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2answers
355 views

Can a detuned laser can excite an atom? How?

Can a detuned laser can excite an atom? If so, how is this possible?
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1answer
335 views

Phase shift in electromagnetic potential

In Aharonov-Bohm effect, how to derive that the wave function of a electric charge $q$ acquires a phase shift $\phi=\frac{q}{\hbar}\int \mathbf{A} \cdot d\mathbf{x}$ after travelling in the non-zero ...
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3answers
4k views

Noether theorem, gauge symmetry and conservation of charge

I'm trying to understand Noether's theorem, and it's application to gauge symmetry. Below what I've done so far. First, the global gauge symmetry. I'm starting with the Lagragian $$L_{1}=\partial^{\...
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2answers
3k views

Do protons exchange photons with electrons?

I'm sorry for this question but, I just don't get it. According to the electromagnetic field theory, electrons repel each other by exchanging photons. How do protons attract electrons, by photon ...
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1answer
2k views

Coherence, Entanglement, Correlation

Let's deal specifically with a two-level system. I understand that ``coherence'' is due to the off-diagonal elements in the density matrix $\rho(t) = \sum_{i}|\psi_i(t)\rangle p_i\langle\psi_i(t)|$ ...
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2answers
266 views

How is the energy/eigenvalue gap plot drawn for adiabatic quantum computation?

I was going through arXiv:quant-ph/0001106v1, the first paper by Farhi on adiabatic quantum computation. Equation 2.24 says, $$\tilde{H}(s) = (1-s)H_B + sH_P$$ which means the adiabatic evolution ...
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2answers
228 views

Cardinality of the Universes Set

No expert by any means, but sometimes, in different contexts the term multiverse used. In quantum mechanics, some say that it is possible that there are actually many universes where all the possible ...
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1answer
239 views

2 following gates, permutation matrix

I have a circuit that has 4 wires and 2 following each other Toffoli gates. I have permutation matrix for each Toffoli gate (A and B). Do I have to multiply that 2 matrices to get the entire ...
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2answers
2k views

Is the movement of electrons truly random?

The result of rolling dice is considered pseudo-random because it depends on an almost endless list of factors (how you roll it, the terrain it lands on, etc.), but it is not TRULY random. Is the ...
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5answers
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Newtonian Mechanics and Quantum mechanics

Why isn't Newtonian mechanics valid in Quantum world? Suppose you isolate an alpha particle and accelerate it in absolute vacuum. Why it doesn't follow the equation $F=ma$? If Newtonian mechanics is ...
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2answers
7k views

Deriving a QM expectation value for a square of momentum $\langle p^2 \rangle$

I alredy derived a QM expectation value for ordinary momentum which is: $$ \langle p \rangle= \int\limits_{-\infty}^{\infty} \overline{\Psi} \left(- i\hbar\frac{d}{dx}\right) \Psi \, d x $$ And i ...
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1answer
198 views

fixed input qubit state to an arbirary pure state using two variable rotations and one fixed rotation

It is a theorem that any arbitrary unitary transformation in SU(2) can be factored into the following form: $ O = U_X(\theta) U_Y(\phi) U_X(\delta) $ Where $U_X$ is a Bloch sphere rotation. I ...
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1answer
303 views

Impulse travelling faster than light [duplicate]

There have been conducted many experiments in which light impulses traveled faster than light like the one in Princeton in 2000. This phenomenon has something to do with quantum entanglement. Does ...
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1answer
599 views

Single photon interference experiment

In short: the question is, does the length of the path affect the outcome of detecting a photon? Consider the single photon beam splitter experiment. Does the probability of detecting the photon ...
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3answers
2k views

Introduction to Anderson localization

I find Anderson's original paper too terse. I am looking for something that introduces me gently to the subject so that I can understand Anderson's paper and other literature. What references are out ...
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6answers
8k views

Probability amplitude in Layman's Terms

I am basically a Computer Programmer, but Physics has always fascinated and often baffled me. I have tried to understand probability density in Quantum Mechanics for many many years. What I ...
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387 views

Entropy of a state subject to the action of a set of random unitaries

Suppose that we have a known set of unitaries $U_1,...,U_n$ randomly selected from the Haar measure and suppose that each unitary is applied with probability $\frac{1}{n}$ to some input state $\rho$ ...
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2answers
1k views

Why does Planck's law for black body radiation have that bell-like shape?

I'm trying to understand Planck's law for the black body radiation, and it states that a black body at a certain temperature will have a maximum intensity for the emission at a certain wavelength, and ...
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2answers
1k views

What is the “direction” of the transition dipole moment? (Understanding Eq. 9.29, Charge and Energy Transfer 3rd Ed, May & Kuhn)

For a real vector $\mathbf{r}$, the direction is given by: $\hat{\mathbf{n}}=\mathbf{r}/\left|\mathbf{r}\right|$. The transition dipole moment is a complex vector. How do you define its direction? ...
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1answer
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The bizarre behaviour of superfluids! Climbing up walls and geting out of glass beakers

SUPERFLUIDITY: Superfluidity is one of the most amazing quantum phenomena, which we can sit and watch them happening before our eyes! Watch this video, it is only a couple of minutes long, which ...
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315 views

Double slit experiments - basic pondering

I have some ponderings about the double slit experiment(s) and mainly their interpretations. Some of my questions may exhibit insufficient scholarship so please bear along, or please point out the ...
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4answers
7k views

Product of exponential of operators

in the context of non-relativistic quantum mechanics I want to show that, for any $A$ and $B$ operators $$e^{A}e^{B}=e^{A+B} $$ if and only if $$[A,B]=0$$ I remember my professor told use about ...
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4answers
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Tunneling v. Hopping

Can someone explain the difference between hopping and tunneling? The context I'm considering is conduction in semiconductors, specifically between impurity states within the bandgap. It's always ...
6
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1answer
619 views

What's vison in Z2 resonating valence bond (RVB) state?

I have a problem on the "vison" exitation in the Z2 RVB state. The vison exitation is a topological exitation of the system like topological defect in nematic liquid , if I got it right. Because the ...
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4answers
1k views

How to prove that the symmetrisation Operator is hermitian?

Let $\mathcal{H}_N$ be the $N$ particle Hilbert space. So a quantum state $\left| \Psi \right>$ may be representated by $$\left| \Psi \right> = \left| k_1 \right>^{(1)}\left| k_2 \right>^{(...
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3answers
869 views

Couldn't we measure electrons with good enough technology? [duplicate]

I am a bit confused about the Heisenberg's Uncertainty Principle - just read about it in How to Teach Physics to Your Dog, by Chad Orzel. He states that the reason electrons can't be measured is ...
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3answers
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Operators explaination and momentum operator in QM

I know and understand why equation below holds. But i am new to operator thing in QM and would need some explaination on this. $$\langle x \rangle = \int\limits_{-\infty}^\infty |\Psi|^2 x \, \...
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4answers
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Validity of naively computing the de Broglie wavelength of a macroscopic object

Many introductory quantum mechanics textbooks include simple exercises on computing the de Broglie wavelength of macroscopic objects, often contrasting the results with that of a proton, etc. For ...
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0answers
16 views

Image formation [duplicate]

What is the real cause behind the formation of an image? It is explained as" when rays of light focus at a point image is formed." So here we have two events, one focusing of light and another ...
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0answers
106 views

2-body interaction energy of 3 particles

If only two-body interaction is considered then what's the energy if I put three particles on one site? Assume delta-interaction and interaction strength is proportional to scattering length $a_F$ ...
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2answers
171 views

Is quantum mechanics similar newtons laws of gravity? In a way [duplicate]

Is quantum mechanics similar to Newtonian gravity in respect that it explains how something works but not why it works? Or does Quantum mechanics explain why it works? (I haven't actually studied QM) ...
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2answers
237 views

How to measure a qubit in a random basis

Let a two dimensional system be in the state $\phi=|0\rangle\langle0|$, for any basis $M$ spanned by the orthogonal vectors $|\psi_0\rangle,|\psi_1\rangle$, we can measure $\phi$ in basis $M$ and ...
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2answers
91 views

What can be the smallest chaotic system?

As I am talking about 'smallest' can I expect that it should be a quantum system? I understand that we use quantum chaos theory instead of perturbation theory when the perturbation is not small. For ...
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Weyl Ordering Rule

While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian $H(...
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2answers
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Quantum Mechanics Notation for BRA KET

I've been given this homework problem, but I do not understand its notation. Please perform the following where the wavefunctions are the normalized eigenfunctions of the harmonic oscillator ...
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1answer
421 views

Find $\hat{x}$ operator given $\hat{p}$ operator

This is problem $1.2$ of Molecular Quantum Mechanics by Atkins, 4th edition. I'm given the momentum operator $$p=\sqrt{\frac{\hbar}{2m}}(A+B)$$ with $$[A,B]=1$$ and I need to find $x$ in this ...
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3answers
148 views

What is this state as a matrix?

In QM I have the state $\lvert 00 \rangle \langle 00 \rvert$. Can anyone tell me what this would look like as a matrix? I know that $$ \lvert 00 \rangle = \begin{pmatrix} 1 & 1 \\ 0 & 0 \end{...