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Questions tagged [quantum-mechanics]

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-theory tag for the theory of many-body quantum-mechanical systems.

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Can we define Spin-Chern number for original QAHE Haldane model?

In Haldane's original paper [5], he discusses the quantum anomalous Hall effect as being characterized by the so-called Chern number that is the surface integral of Berry curvature over the entire ...
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Is the Process of Projection of a Generic State Onto a Subspace Impossible? [closed]

I can define (in a standard way) the process of projection of a generic state onto the subspace $\mathcal{G}$ as a process that takes a generic state $|\psi\rangle$ of the Hilbert space $\mathcal{H}$ ...
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Are the microwaves in an ECRIS plane polarized?

Or randomly polarized? Are the photons in phase, like in a laser or maser? What is the theory behind how an electron in an ECRIS responds to a microwave photon?
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Delta function eigenstate for non-zero potential

Consider the potential $V(x)=\frac{2}{x^2}$ and let $\frac{\hbar^2}{2m}=1$ for convenience. Now consider the function $\psi(x)=\delta(x)$. According to Griffiths (electrodynamics book) problem 1.45(a),...
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Momentum conservation in Quantum Mechanics

Most quantum mechanical potentials are not translationally invariant and therefore the expectation value of momentum varies. The question is then where has this momentum been transferred to? Because ...
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How to numerically calculate the transition dipole integral in periodic systems? [migrated]

Now I have wave functions $\psi_a$ and $\psi_b$ of two states in Gaussian CUBE format. I'd like to evaluate the transition dipole moment integral $\pmb\mu$ between these two states. As my simulation ...
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Why do bosons tend to occupy the same state?

It is often said that, while many fermions cannot occupy the same state, bosons have the tendency to do that. Sometimes this is expressed figuratively by saying, for example, that "bosons are sociable"...
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Manipulation of composite density matrices (operators)

Suppose we have two systems with density matrices $\rho_1$ and $\rho_2$. Initially they are non-interacting, and so their composite density matrix looks like: $$\rho_t = \rho_1 \otimes \rho_2$$ I ...
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Driving force and mean of a particle wave function [duplicate]

I am currently undergoing a course on introduction to quantum mechanics and we took the historical approach. I'm currently at DeBroglie wavelength. He introduces the wave particle duality in matter, ...
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Fermi golden rule: occupation factor

Fermi's golden rule for transitions between single-particle states $a$ and $b$ is $$ \Gamma_{ a \to b} = \frac{2\pi}{\hbar}\vert M_{ab} \vert^2\delta(\epsilon_a - \epsilon_b) \, .\tag{1} $$ Here $\...
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Does quantization go from quantum $\to$ classical or the other way around?

I was thinking about the relationship of classical mechanics to quantum mechanics, as I just took my first course in quantum mechanics. My specific question was about quantization. For a harmonic ...
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Imaginary energy integration

Is it possible to solve the integral: $$ \int_{-\infty}^{\infty} \frac{e^{ixs}}{k^2-s^2}ds $$ if it is known that $k^2$ has infinitesimal imaginary part (proportional to energy of a quantum ...
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Particle in an infinite potential region [duplicate]

In an infinite square well, problem with the following set up $$ V(x) = \begin{cases} 0 &\text{if }0 < x <L \\ \infty &\text{if }x <0 \ \text{and} \ x>L \end{cases} $$ it is ...
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How can electrons travel from the valence band into the conduction band?

I'm currently studying Introductory Semiconductor Device Physics by Parker. In band-theory, we know that if an electron is at the top of an energy band, then there are no allowed states immediately ...
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Is there a way for light to be reflected out of the usual plane of incident?

Is it possible for use to apply a potential or magnetic field to the surface of the media, so that the light being reflected out of the plane of incident? i.e. Compare to an initial "vertical" plane ...
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Mathematical aspects of decoherence

I am trying to understand the maths behind decoherence. I first state the framework I am working with, and then I ask my questions. Let $H_A$, $H_B$ be finite dimensional Hilbert spaces ("the system" ...
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1answer
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Quantum mechanics on operator [closed]

If any operator is commute with Hamilton then they are labelled such a way that the energy eigenstate are equal and we also know it is a constant of motion. I don't related constant of motion with ...
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Can Schrödinger's cat be revived?

According to Quantum Mechanics, Schrödinger’s cat is in a superposition state of $\frac{1}{\sqrt{2}}(\left|A\right> + \left|D\right>)$, where $\left|A\right>$ and $\left|D\right>$ ...
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1answer
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Probability of finding hydrogen atom in its ground state given an initial state

So I came across this question that asked what is the probability of a hydrogen atom which is prepared in an initial state $\Psi (\vec{r},t)$ to be in the ground state $\psi_{100}(\vec{r}) =2exp(-r)Y_{...
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Insert a Unitary operation between two others [migrated]

Let's say I have two unitary operations $U_1$ and $U_2$, which together give a rotation of the following form: $$ U_1\cdot U_2 = \begin{pmatrix} e^{i\varphi} & 0 \\ 0&e^{-i\varphi} \end{...
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Bosonic Pair Distribution Function

In Schwabls Book "Advanced Quantum Mechanics" in the chapter for Bosons he calculates the Bosonic pair distribution function for noninteracting bosons. He said the expectation value of \begin{align*} \...
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What happens to the central bright fringe if the overlapping of the waves in phase do not happen crest on crest

In a Young's double slit experiment,we get the central bright fringe in the middle of the screen taking that the waves coming from the slits being in phase overlap each other with crest on crest or ...
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Linear response treatment of the magnetization of a system of noninteracting fermions

While trying to solve an exercise, I ran into what looks like a contradiction. I'm sure I'm making some kind of mistake, but I couldn't spot it. I'm not asking for help in solving the exercise, which ...
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1answer
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Bose-Einstein distribution and magnons

I have some doubt about the Bose-Einstein distribution for magnons/spin-waves. A one-dimensional ferromagnet placed in an external magnetic field $\mathbf{B} = B\, \hat{z}$ obeys the Hamiltonian $$H ...
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1answer
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How are contextuality and locality related?

I know how quantum non-locality is defined in Wikipedia quantum nonlocality is a characteristic of some measurements made at a microscopic level that contradict the assumptions of local realism ...
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Electrons Fired One at a Time in Double-slit Experiment

I have read that electrons fired individually through a 2 or more slits still form an interference pattern. I think this may be due to the fact that moving electrons produce electromagnetic waves (...
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Can bipartite mixed entangled states show Hardy nonlocality?

I understand that apart from maximally entangled states, all pure entangled states yield Hardy correlations for certain measurement settings. Can the same be told for mixed entangled states?
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How do we know which states are decohered by the environment?

If I take an atom in a momentum eigenstate, or just a very narrow gaussian in momentum space (with a very large spread in position space), and then I throw it into a gas, it will quickly decohere into ...
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How an operator is converted to a function? [closed]

$$\langle m|F|n\rangle^*=\langle F(n)|m\rangle$$ How does the operator become a function of state $|n\rangle$?
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3answers
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What is the difference between Statistical Mechanics and Quantum Mechanics [closed]

What is the difference between Statistical and Quantum Mechanics? In both we try to study the property of small particles using probability and hence apply to macroscopic systems.
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1answer
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Angular momentum and Zeeman effect

Supposing an Alkali atom positioned in magnetic field in $z$-axis. I understand linearly polarized laser propagating in $z$-axis can induce $\sigma$ transmission. But I could not figure out how laser ...
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Angular Momentum Coupling and 3jm Symbols

I have a question regarding j coupling. At the moment, I try to learn the diagrammatic approach which is written down in Varshalovich, Chapter 11. But there I have now a question regarding the ...
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Matter waves properties [duplicate]

In classical waves, there is always something that is'waving Thus in water waves the water surface moves up and down, in sound waves the air pressure oscillates and in electromagnetic waves the ...
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Can the Dirac quantization condition be derived within Lev Vaidman's formalism without gauge fields?

Textbooks often claim that phenomena like the Aharonov-Bohm effect require that any local formulation of quantum gauge theory use gauge potential fields. (It's also sometimes claimed that the A-B ...
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1answer
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Can a single photon behave in a non-local way?

Most discussions of quantum non-locality center on entangled pairs of particles which are described by a single wave function and thus, in some way, are to be regarded as one quantum object such that ...
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1answer
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Comparing measurements of a 2D quantum harmonic oscillator between cartesian and rotated cartesian coordinates

I've come across an old quantum exam problem that's causing me a bit of confusion, and I'm hoping someone can offer some clarity: There is a particle in a 2D harmonic oscillator potential such that ...
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1answer
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How to calculate second-order correction to the energy from matrix elements of perturbation?

A particle is in the one dimensional harmonic potential $V(x)=\frac{1}{2}m\omega^2x^2$ with a small perturbation $V'$. I want to calculate the first- and second order correction to the ground state ...
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Intuition behind quantum CNOT gate applied to a pair of electrons [duplicate]

I'm looking for some intuition behind how a cNOT gate works. I think I understand the mathematics; but, I'm having trouble imagining how two electrons would interact to produce the predicted result. ...
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1answer
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Intuitive “story” explaining how orientation of spin axis affects up/down observation?

Is there a "convenient fiction" that explains why the angle of an electron's spin axis affects the probability of it being observed in a spin up or spin down state? By "convenient fiction", I mean a ...
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Fundamental thermodynamic relation for discrete quantum partition function (density matrix)

In the case of a discrete classical partition function defined as: $$ Z=\sum_{q \in Q}e^{-\beta (E(q)+pV(q))} $$ It is straightforward to show that it implies the following fundamental thermodynamic ...
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1answer
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Quantised energy levels of the nucleus

We know that the atomic energy levels are quantised since the nucleus has a potential of its own and solving the Schrödinger equation we can see that. But in gamma emission we see that the origin of ...
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1answer
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Electrons in a conductor loosely bound or delocalised (as per QM)?

Currently there are two main ideas of those electrons that move in a conductor: those electrons moving are loosely bound to the valence shells of the atoms in the lattice those electrons moving are ...
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Is reality really epistemological in its complete sense?

Taking the case of Schrodinger's cat, if the measurement of the cat is not yet done, then I don't know whether the cat is dead or alive. Epistemologically speaking, since I don't know about the ...
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Finding the eigenstates of an operator [closed]

I am currently taking a course in QM and can't see how the eigenstates have been found for examples like this one: Question Let $\phi _1$ and $\phi _2$ be two normalised wavefunctions orthogonal onto ...
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1answer
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Qualitative understanding of negative step potential problem

In QM textbooks the single step potential problem is explained in great detail. However, it is hard to understand what happens when $V_{0}<0$. Could anyone please explain qualitatively, how the ...
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1answer
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De Broglie explanation of Bohr's second postulate. discrepancy of 2 times?

I am reading how de Broglie justified the 2nd postulate of Niels Bohr (i.e. angular momentum of an electron to be integral multiple of $\frac{h}{2\pi}$). I get his explanation of electron acting like ...
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transmission coefficient and transmission probability

Are transmission coefficient and transmission probability the same terms? If not, could you please explain how they are related to each other?
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Why are systems in classical mechanics sets and not vector spaces?

One of my professors told me that a state in a classical system is an element of a set, while in quantum it's an element of a vector space. From that, we combine systems in classical physics using a ...
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quantum mechanical treatment of rayleigh scatterring

Is there a quantum mechanical explanation of light scattering by atmospheric gases? Classically, treating the atmospheric particles as excited dipole antennas, we know that the amount of scattering is ...
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State change and probability of measurement

Could anyone please confirm if the following reasoning is correct? When a hermitian operator $\Omega$ has two eigenkets $\left|a\right>$, $\left|b\right>$, and Hamiltonian H has eigenkets $\...