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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Quantum Wave Mechanics

I am studying QM-I these days. Now, I just think of the wave function as just a mathematical function that defines the state of the particle at an instant and from it you can extract various ...
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3answers
205 views

Entanglement in single particle state

Is it possible that we have entanglement in different degrees of freedom of a singe particle. like spin and linear momentum .
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1answer
2k views

Calculating the energy of an electron given the wavelength

Okay, so I know that the wavelength of an electron is 5e-7m and I am asked to calculate its minimum velocity and hence minimum energy. Calculating the minimum ...
1
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1answer
159 views

Heisenberg picture usage - Merzbacher 14.106

I am trying to understand a line in the quantum mechanics book by Merzbacher, specifically the second line of equation 14.106. The problem is a forced quantum harmonic oscillator. The Hamiltonian ...
2
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2answers
166 views

A black torch to darken everything

Can we ever have a black colored (the color of the light and not the body's color) torch that darken (or dis-illuminates) everything? While compared to a normal torch it would function in an opposite ...
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1answer
88 views

Info request on studying QIT/QIS or QM with a Computer Science background [closed]

I've been considering a career change for a long time and recently discovered the Two-Slit Experiment, which, to put it frankly, blew my mind. I then started some hefty reading and investigation into ...
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2answers
110 views

energy of electrons outside an atom

The higher the quantum number(energy levels)m the higher the energy. What does the energy refers to? Kinetic energy, potential energy, or the total mechanic energy?
2
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1answer
130 views

Which types of particles are affected by the wave-particle duality?

If we take the double slit experiment as a way of demonstrating the wave-particle duality, which types of particles would show an interference pattern? For example, I know that electrons show such a ...
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0answers
231 views

Why do some terms vanish in first-order perturbation theory?

In first order perturbation theory, we usually express the first order perturbation in the eigenket of the perturbed Hamiltonian in the basis of the unperturbed Hamiltonian $H_{0}$: ...
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1answer
67 views

Positron and other particles [closed]

Positron is a particle which has the same mass as an electron . But it has positive charge on it . When electron and positron combine, they annihilate each other with the release of energy in the ...
2
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0answers
59 views

Applications of Quantum Walks [closed]

Can someone explain to me what real world applications could potentially benefit from the study of quantum random walks? I have researched a fair amount on how quantum walks operate and their ...
2
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0answers
146 views

leaving 2-norm propelled probability implications

I am curious about why there are no further generalized probability structures used in Physics. The great revolution was moving away from one-norm system to a two-norm system. What happens if we ...
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0answers
114 views

Test for Many Worlds Hypothesis

If one actually ran an experiment similar to the Schrodinger's cat thought experiment, and ran it enough times (with the same cat) to get the confidence interval good enough, could one say that ...
2
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1answer
2k views

Two ways of calculating the expectation value of momentum

The expectation value of momentum is given by: $$ \langle p\rangle = \int_{-\infty}^{\infty}\psi^{*}(x)\left(-i\hbar\frac{\partial}{\partial x}\right)\psi(x)dx $$ How can I show that the above ...
3
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1answer
83 views

Mutually unbiased bases

This question can be formulated in two ways. Let there be two $d$-dimensional orthonormal bases $B_{1}$ and $B_{2}$. I refer to the elements of $B_{1}$ by $\lvert\nu_{i}\rangle$ and to the elements of ...
0
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1answer
99 views

Group velocity of localized wavepacket

This is a Homework problem so please feel free to not answer and just give pointers. A localized wavepacket is given as: $$\Phi(r,t=0 ) = \frac { e^{-\large\frac {r^2}{2s^2}} e^{\large\frac{i\pi ...
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0answers
465 views

Is non-relativistic quantum field theory equivalent with quantum mechanics?

Related post Can we "trivialize" the equivalence between canonical quantization of fields and second quantization of particles? Some books of many-body physics, e.g. A.L.Fetter and ...
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1answer
469 views

Writing an arbitrary operator in bra-ket notation

An annoying fact about my physics textbook (Griffiths' Introduction to Quantum Mechanics) is that it introduces bra-ket notation without telling us how to use it. So I have a two-part question for SE: ...
3
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1answer
434 views

QM: How to compute position/momentum relation in polar coordinates

So if we are working in one dimensional space, we have the formula: $$\langle x|p\rangle = \frac{1}{\sqrt{2\pi\hbar}} e^{ipx/\hbar}$$ Suppose instead we are confined to a circle of radius $R$ so that ...
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2answers
114 views

Regarding derivation of Probability Current

The question for the full derivation of Probability Conservation -> Probability Current was already asked here: Probability current. I apologize for not retyping it out, but it's already beautifully ...
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2answers
194 views

When do we see particles to be in a superposition of energy states?

I have two doubts: Exactly when does this happen? and If we are in a superposition of states (lets say E1 and E2) and the particle absorbs a photon, what will happen? If E3-E1 = hf, will it go to E3? ...
12
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2answers
358 views

Particle/antiparticle annihilation and entanglement

This is a basic question. Suppose that A and B are completely entangled particles and so are C and D. If B and C are antiparticles that annihilate each other will A and D be entangled as a result. It ...
3
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1answer
257 views

Electrons skip randomly around their orbits

I read where the electron (as well as a few other particles) skips around in its orbit randomly rather than move around the orbit smoothly. This effect has been repeatedly observed in the laboratory ...
2
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5answers
993 views

How to derive Schrödinger equation?

How is the Schrödinger equation $$\frac {\partial }{\partial t}\psi=-\frac {i }{\hbar }H{\psi }$$ being derived?
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0answers
323 views

Born approximation to Lippmann-Schwinger integral equation

I am having the following problem understanding the Born approximation in the case of the Lippmann-Schwinger equation. This exercise is for something which is entitled "computational physics lab ...
2
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1answer
431 views

Derivation of existence of energy band gap in semiconductor (solid State)

I am looking for both a mathematical and a physical reason for energy band gap in metals. For Physical reason, I was told that at each reciprocal lattice, you could have Bragg scattering, that would ...
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0answers
1k views

Numerical problem in solving the Bogoliubov de Gennes equations- methods to solve?

I am trying to solve an assignment on solving the Bogoliubov de Gennes equations self-consistently in Matlab. BdG equations in 1-Dimension are as follows:- $$\left(\begin{array}{cc} ...
4
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2answers
199 views

Electron speed in Atoms

Is the speed of electrons in Atoms consistent in all Atoms or clusters/groups/individual elements, and if it is consistent in any atom, is that speed constant?
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1answer
94 views

Conduction and propagation [duplicate]

What is the difference between conduction of electric wave in conductor and propagation of electromagnetic wave in dielectric? Why propagation term is used for dielectric and conduction for ...
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0answers
122 views

Interesting Harmonic Oscillator Solution

On page 89 of Griffith's QM book, an exact solution to the time-dependent SE equation for the harmonic oscillator is mentioned: $$ ...
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1answer
771 views

Relating Schrödinger's Wave Equation and Heisenberg Uncertainty Principle

A homework question that I don't conceptually understand: A quantum particle of mass M is trapped inside an infinite, one-dimensional square well of width $L$. If we were to solve Schrodinger's wave ...
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1answer
98 views

How to find different operator representations in QM?

I read that any observable operator may be represented as: $$\Omega = \sum_n \omega _n | \omega _n \rangle \langle \omega_n |$$ Where the little omegas are the eigenvectors/eigenvalues of the ...
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0answers
50 views

Physical interpretation of Fermi golden rule? [duplicate]

What is the physical interpretation of Fermi's golden rule?
14
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1answer
1k views

Self-adjoint and unbounded operators in QM

An operator $A$ is said to be self-adjoint if $(\chi,A\psi)=(A\chi,\psi)$ for $\psi, \chi \in D_A$ and $D_A=D_{A^\dagger}$. But for the free particle momentum operator $\hat{p}$ these inner products ...
2
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0answers
44 views

Two identical particles with spin $s$. What is the spin of its corresponding “center-of-mass” and “relative” particles?

Consider a system of two identical quantum particles with spin $s$ and mass $m$. Using center-of-mass coordinates one obtains an equivalent system given by a particle of mass $2m$ and one of mass ...
12
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1answer
519 views

Quantum computing records (entangled qubits)

What is the current record number of entagled qubits and how has this number been increased? The latest result on stack exchange, which is 3 years old, reports 14 via this post: How many stabilised ...
15
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6answers
2k views

Are there forces which do not involve a change in momentum?

I am familiar with the equation $$\vec{F}=m \vec{a}$$ I am wondering as to whether it is possible for something to exert a force on another object without changing the momentum of said object. My ...
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0answers
103 views

Basic concepts in quantum theory to start learning semiconductor physics [closed]

What basic concepts in quantum theory one must known to start learning semiconductor physics?
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0answers
92 views

group velocity VS probability current

Think about an electron been accelerated from rest in a static electricfield. If we treat the problem classically, in which the electron is just a point charge. The velocity of the electron would ...
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0answers
91 views

Questions on electron orbits

I have three questions to ask: Why do electrons (in an atom) specifically move in orbits and not some other type of motion? Where does the energy comes from, for the electron to move at much higher ...
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3answers
2k views

Why not drop $\hbar\omega/2$ from the quantum harmonic oscillator energy?

Since energy can always be shifted by a constant value without changing anything, why do books on quantum mechanics bother carrying the term $\hbar\omega/2$ around? To be precise, why do we write $H ...
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3answers
949 views

Schrödinger's Equation and the depth of a finite potential well

Before I ask my question, I have to stress: I have absolutely no idea what the math is going on. I've read my textbook, several Wikipedia articles, scoured the internet, and don't feel anymore ...
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1answer
100 views

Quantum State Function $\psi$

If I write in QM at an instant, that the quantum state that describes the particle completely at an instant $\psi(x)=\cos(6\pi x)$. Does that mean $|\psi(x)|^2dx$ after normalisation gives me the ...
4
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1answer
472 views

Does limit $\hbar \rightarrow 0$ in Quantum Mechanics mean anything? [duplicate]

Assuming that I learn Quantum Mechanics first, and then I approach Classical Mechanics as a special case of Quantum Mechanics, I will definitely find the relationship between Quantum Mechanics and ...
0
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1answer
142 views

black body radiation graph [duplicate]

I got really confused about the graph of the relationship between wavelength and intensity of black body radiation. What does the peak stand for? And what does the graph tell us?How can we analyze it? ...
0
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1answer
113 views

Relation between different quantum excitation energy, mass energy and kinetic energy

When a particle enters an excited state, the energy appears in its quantum wavefunction according to $E = h \nu$. Does the $E$ in this equation also include kinetic energy, and rest mass energy? ...
0
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1answer
100 views

Doesn't the uncertainty principle mean all particles with identical energy are indistinguishable and hence have an amplitude for exchange?

I wonder if someone could tell me where my logic is going wrong here? If two particles both have definite energy, then they have indefinite position. As their positions could literally be anywhere ...
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0answers
56 views

How does a complex wavefunction “hold” energy?

Feynmann Lectures Vol 3 Ch 8 Sec 6 describes how an ammonia molecule can have two definite energy states. If the amplitudes of the base states are $ C_1(t) ...
1
vote
1answer
103 views

What prevents the nucleus from wandering into the electron cloud?

I have seen the question about why the electrons don't fall into the nucleus, and I understand that completely. However, the converse of this question is very interesting as well: "What prevents the ...
0
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1answer
229 views

Valley meaning explanation for foreigner

English is not my native language and I have some hard time translating this word. I was searching in couple dictionaries(both paper and online) and could not find it. Could anyone provide me ...