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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58 views

If I were to keep increasing the mass of particles I throw at a double slit, at what point would it stop creating an interference pattern? [duplicate]

Why don't things like tennis balls create interference patterns when thrown at double slits? Where's the limit where it stops interfering?
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1answer
62 views

Meaning of “vacuum state”?

I just learned about $|0\rangle$ and siblings $|0_\gamma\rangle$ and $|0_\infty\rangle$ while studying coherent and squeezed states in a QM class, and I have a question about the meaning of ...
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2answers
80 views

Could Quantum Entanglement be related with gravitational interactions? [closed]

Particles are entangled when they share the same state and their properties become correlated. Interaction with one of them, by say measurement, is experienced instantly by the other. If we measure ...
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1answer
311 views

What is a 'turning point' in WKB and why does it fail at that point?

What is meant by a classical turning point in quantum mechanics and why does the WKB approximation fail at that point?
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2answers
83 views

How do I prove that the del squared operator commutes with the angular momentum operator? [closed]

I need to prove in Cartesian coordinates that $[\nabla^{2},\hat{L_{z}}]= 0$ I know that the angular momentum operator is defined as: $\hat{L_{z}}=x\hat{p_{y}}-y\hat{p_{x}}$ And the del squared is ...
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1answer
66 views

Anticommutator difference [closed]

What is the value of this difference of anticommutators $$\{x^2,p^2\}-(\{x,p\}^2)/2$$ if the commutator $$[x,p]=i\hbar ~?$$ I have tried and obtained a value $$-3\hbar^2/2 - 2i\hbar px.$$ But ...
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0answers
31 views

Principle behind Atom Interferometry?

In Laser Interferometry, you propagate a laser beam, split it into two different paths, reflect once, combine it back and deduce the phase difference accumulated from the path difference, from the ...
2
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0answers
29 views

What physical effects cause materialization of a system of particles for a short time?

It is well-known from physics that a photon with enough energy creates a pair of particles: one electron and one positron. This pair of particles can only exist for a short time. This process is ...
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34 views

commutation relations for operators in projected subspaces

I am looking for a consistent re-definition of commutators for certain operators when I work in a projected subspace. Basically, I have a spin defined in terms of 4 Majorana operators $b_{x}$, ...
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2answers
57 views

Schrodinger field and klein gordon field

In the usual Fourier expansion of schrodinger fields \begin{align} \Psi(\vec{x}) = \frac{1}{(2\pi)^{\frac{3}{2}}} \int d^3 k \hat{a}_k e^{-i (wt-\vec{k}\cdot \vec{x})}, \quad \Psi^{*}(\vec{x}) = ...
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0answers
19 views

Energy-level choice for electron at photon emission [duplicate]

An electron absorb a photon and jumps to the last energy level.Now when it goes done,How does it choose which level it will step down to?.Also I've come to now that it can omit one step(e.g from 5th ...
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0answers
78 views

Prove that $e^{\frac{i\lambda}{\hbar} S_x}S_ze^{-\frac{i\lambda}{\hbar}S_x}=S_z\cos(\lambda)+S_y\sin(\lambda)$ [closed]

Prove using Hadamard's lemma that $$e^{\frac{i\lambda}{\hbar} S_x}S_ze^{-\frac{i\lambda}{\hbar}S_x}=S_z\cos(\lambda)+S_y\sin(\lambda) $$ where $\lambda$ is a complex number. I get: ...
3
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2answers
60 views

How is CNOT operation realized physically?

I think I understood very well how operations on one qubit are done - if qubit is electron, we just apply magnetic field in direction we want to make spin precess (unitary operations on single qubit). ...
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0answers
40 views

Do interaction free experiments violate Quantum Physics?

Although I know that interaction free experiments come under Quantum Physics, Don't the kind of violate the Heisenberg uncertainty principle? Because you get a value without interacting with the ...
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2answers
99 views

Is teleportation possible?

When I just learned about quantum entanglement, I read that if two electrons are in quantum entanglement and placed in two different places, the photon which interacted with one electron is teleported ...
2
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1answer
88 views

Is de Broglie matter wave a mass or a particle hypothesis?

I'm having difficulty understanding de Broglie matter wave hypothesis. It is a mass or a particle hypothesis? According to de Broglie a particle with mass $m$ moving at a constant speed has an ...
0
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1answer
89 views

Prove that $(e^{i\lambda A})^\dagger=e^{-i\lambda A^\dagger}$ [closed]

Prove $$(e^{i\lambda A})^\dagger=e^{-i\lambda A^\dagger}$$ where $A$ is an operator. Can anyone explain how to go about this question? Writing it as a power series gets confusing. So basically I ...
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1answer
28 views

Quantum harmonic ocillator and the mean energy U(T)

The energy of a quantum harmonic oscillator is given by: $$E(n)=\hbar\omega\left(n+\frac{1}{2}\right)$$ The canonical partition function is given by: $$Z(T)=\sum_{n=o}^\infty e^{-\beta ...
2
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1answer
58 views

Can All 4-D column matrices be given as tensor product of 2-D column matrices?

I am familiar with entanglement concept. But it feels bit weird to me that all possibilities of a system in a $4$-dimensional vector space cannot be given as tensor product of two $2$-dimensional ...
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2answers
79 views

What is the correct quantization of Hamiltonians of the form $H=x·p$ whose naive quantization is not Hermitian?

As we all learn in Basic Quantum Mechanics (the first quantization), we promote the classical variables to operators. Say, the classical hamiltonian $\frac{p^2}{2m}+V(x)$ to ...
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0answers
33 views

A question on intermediate step in deriving gravitational anomaly by Fujikawa's method

In Fujikawa's 'Path integrals and Quantum Anomalies', Eq.(10.26) in the derivation of gravitational anomaly in Chapter 10.1 is puzzling for me. ...
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1answer
59 views

Difference between quantum numbers j and m and the four others

I am confused about what is the difference between the quantum numbers $j$ and $m$ and the other four quantum numbers: the principal quantum number $n$, angular momentum $m$, etc.? From Quantum ...
2
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1answer
40 views

Charge density of an atomic orbital

Chemistry textbooks on atomic orbitals typically start off with the concept of electrons (viewed as negatively charged point-particles) moving around the nucleus, attracted and bound by the Coulomb ...
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1answer
24 views

Photoelectric effect and work function relation

Let's consider the graph above for two metals $M_1$ and $M_2$ showing relation between photocurrent and potential. First question that I want to ask here is that how do you relate stopping ...
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47 views

How to calculate the expectation value of position/momentum using path integrals?

We have the formula: \begin{equation} \langle F \rangle = \frac{\int Dx \times F[\phi] exp\{i/\hbar S[\phi]\}}{\int Dx \times exp\{i/\hbar S[\phi]\}} \end{equation} Now, I am wondering how a change ...
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1answer
60 views

Covariance of the Dirac Equation

i want to show that the following equation holds: $$ \frac{1}{8}\left[\gamma^{\mu},\omega_{\mu \nu} [\gamma^{\mu},\gamma^{\nu} ] \right] = \omega^{\mu}_{~~~\nu}\,~ \gamma^{\nu} $$ $\gamma^{\mu}$ ...
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1answer
47 views

How to calculate the expectation value of position vector?

$$\psi (\vec{x})=Ae^{-(1/4a^2)|\vec{x}-\vec{x}_0|^2}e^{i\vec{p}_0\cdot \vec{x}/\hbar}$$ The wave function is like this, then how is the expectation value of position vector (not position) calculated? ...
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0answers
13 views

plane wave state used for scattering calculation

When we do scattering calculation off a potential barrier, normally we would assume some incident plane wave and then make use of the boundary conditions. But how is this corresponding to the ...
1
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1answer
88 views

Quantum anharmonic ocscillator $E_0(\lambda)$ curve or table

I am looking for the exact data on $E_0(\lambda)$ for the anharmonicity $\lambda x^4$. The perturbative expansion is the following: $E_0(\lambda)\approx 0.5(1+1.5\lambda -5.25\lambda ...
0
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2answers
49 views

One dimensional scattering cross section

My quantum mechanics book (http://www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf, pages 94-95 of the pdf, or 86-87 of the book) considers the one dimensional step potential ...
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2answers
66 views

How does light oscillate?

Why do we say that electromagnetic wave is oscillating? Or does light propagate really in a wavy form like this image? What is making the photons oscillate and how is it oscillating is it ...
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0answers
23 views

What are the reactions that take place inside battery at the quantum level?

I was just studying about how a battery works on the internet and found out that there are reactions of chemicals which make the electrons move. But what exactly happens inside a battery (lets take a ...
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2answers
49 views

Is it possible to make an electromagnetic shield?

Is it possible to make an electromagnetic shield to protect something (or ourselves) against things like bullets, human attacks, metals thrown on us or simple dust particles to protect a spaceship ...
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0answers
68 views

How can we prove this system is in a stationary state?

I'm having trouble using the given hint to solve the problem. The problem statement is as follows: At instant $t=0$, the probability distribution of a particle under a potential $V(x)$ is ...
0
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1answer
37 views

How to solve infinite square well with exponential solution (of oscillatory type)?

Given a potential well of $V = 0$ on the interval $(0,L)$ and $V = \infty$ outside the well, I am working to solve the Time Independent Schrodinger Equation $$\dfrac{d^2}{dx^2} \psi= ...
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1answer
49 views

Can an Atom be negatively as well as positively charged simultaneously?

For example there are three atoms- atom A, atom B, atom C. Atom A has 3 electrons, atom B has 4 electrons and atom C has 2 electrons. If we bring together atom A and atom B, in this case atom A is ...
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0answers
29 views

Accuracy of quantum mechanical algorithms

Is it possible for a quantum mechanical algorithm to ensure when the wave function collapses that the right answer will be obtained 100% of the time? For this, I am excluding processes such as ...
2
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2answers
132 views

The equivalence between Heisenberg and Schroedinger pictures

In quantum mechanics, the two pictures of Schroedinger and Heisenberg are taken as equivalent, where in the former wavefunctions are time variants and operators are not, and in the latter it is the ...
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2answers
84 views

Does a photon travel in all directions?

For example i am standing and a beam of light is passing in front of me. I am able to see that beam of light so does it mean that photons are travelling in all directions other than the photons which ...
0
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2answers
53 views

Is the interference quantum mechanical superposition the same as entanglement? [duplicate]

Are the interference of two wave functions an equivalent way of saying that they are entangled?
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0answers
20 views

Orthogonality preservation vs. preparing a state

I'm trying to learn the fundamentals of quantum theory, lately mostly using the lectures by Prof. Susskind which Stanford University made available on Youtube. Here is one thing I have trouble ...
2
votes
2answers
83 views

What is the Hermitian adjoint of operator $\hat{K}\psi = \psi^*$?

For many operators, their adjoint can be expressed as a function of other known operators, for example $$\hat{T}_a^\dagger = \hat{T}_{-a} \\ \hat{p}_x^\dagger = \hat{p}_x$$ where $\hat{T}_a \psi (x) = ...
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0answers
25 views

Valence bond wavefunction of nitrogen

Could someone explain to me how one finds the valence bond wavefunction of an atom? Take nitrogen for example, I know both nitrogen molecules have a valence-electron configuration of 2s22p1x2p1y2p1z ...
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0answers
10 views

Stress testing Quantum Uncertainty, a multi Phase Question

I start this line of thinking, and i begin to seek the right questions to ask. I am of humble origin, but even here i remember that all start small somewhere. I think that even the greatest minds ...
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3answers
70 views

What is $E$ in the Planck-Einstein relation?

The Planck-Einstein relation was first given for photons $$E = h\nu$$ But later, de Broglie extended it to matter waves, and showed that it would hold for all particles as well. The $E$ for a photon ...
2
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1answer
32 views

How to pull out the momentum operator?

In the equation (1.7.17), how does operator $p$ get out of the bracket without any operation though $<a | $, $| x'>$ are function of $x'$? How to prove this?
3
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1answer
47 views

What are these wavish patterns around atoms on microscopic images?

This is an IBM movie about how they move single atoms: http://www.youtube.com/watch?v=oSCX78-8-q0 There are often some "wavish" pattern around atoms on these pictures, like below some of them marked ...
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3answers
133 views

Violation of Pauli exclusion principle

From hyperphysics (emphasis mine): Neutron degeneracy is a stellar application of the Pauli Exclusion Principle, as is electron degeneracy. No two neutrons can occupy identical states, even under ...
0
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1answer
72 views

Why does this resource say that the Schrodinger Equation can be derived? [duplicate]

http://arxiv.org/abs/physics/0610121 If this is true, why do resources say that it cannot be derived? If it isn't true, can someone explain where the above preprint is wrong? I believe that my ...
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1answer
28 views

Is there an implicit assumption that each quantum well contains a single electron only? [closed]

Is it true that each electron can be represented as a quantum well? I had believed that each energy level was able to contain multiple states and each states were able to hold multiple electrons.