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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Spontaneous emission and coherence

Assume I prepare a linear superposition $\frac{1}{\sqrt{2}}(|g \rangle+|e\rangle)$ between a ground and excited level for a large number of "atoms" (it can by any multilevel system, not ...
Alex Marshall's user avatar
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Probability for error correction of phase flip error

I study by myself with books about error correction. I read about 'three qubits error correction', and I try to think about the change in the probability to get error. Let's say that the probability ...
Yohay Halfon's user avatar
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Are there proofs by contradiction in physical theories? [closed]

I am interested in whether there is such a thing as a proof by contradiction in physics, especially fundamental physical theories like QM or GR. I am just being curious, and I haven't been able to ...
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Quantum interference : an instantaneous consequence of superposition? [closed]

Is quantum interference a process that takes place over time, or an instantaneous consequence of superposition?
Husserliana's user avatar
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Momentum Eigenvalues for Particle in a Box

A question from my college exams is as follows: Find out the eigenfunctions and eigenvalues of the momentum of a particle of mass $m$ moving inside an infinite one-dimensional potential well of width ...
L lawliet's user avatar
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Using Galilean covariance to find conditions on physical observables

Let's suppose that coordinates have to transform accoring to the Inhomogenous Galilean Group. Then $$ x' = x + a + v(t+b) $$ $$ t' = t + b $$ Let's use a funtion $\psi(x,t)$ of $x$ and $t$ as the ...
Ilya Iakoub's user avatar
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What's wrong with my solution? Infinite wall and delta barrier scattering [closed]

We have the potential $$V(x)=\begin{cases}\infty & ,x \le 0 \\ V_0\delta(x-a) & ,x>0\end{cases}$$ The problem is to find the amplitude of scattered wave and to analize the phase shift ...
Andrew Glatten's user avatar
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How to deal with explicit time dependence in the Heisenberg picture?

I am studying for my test in Quantum Mechanics, and there is something I don't quite understand about the Heisenberg picture and Heisenberg's equation of motion. In the lecture, we derived Heisenberg'...
Shai Avr's user avatar
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Clarification on Transforming from Discrete to Continuous Systems in Quantum Mechanics [closed]

In Quantum Mechanics: A Paradigms Approach by David H. McIntyre, a transformation from discrete systems to continuous ones is provided, outlined as follows: $\vert\psi\rangle \rightarrow \psi(x)$ $\...
GedankenExperimentalist's user avatar
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Symmetry transformations in C* formulation in quantum mechanics

In the normal Hilbert space formulation of quantum mechanics, symmetry transformations are represented by unitary (or antiuntitary) operators that act on a Hilbert space. So my question is: How can ...
Monterosa2's user avatar
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Reciprocity theorem of reaction cross section

The reciprocity equation for reaction cross section reads $$ka^{2}\sigma_{ab}=kb^{2}\sigma_{ba}$$ or $$pa^{2}\sigma_{ab}=pb^{2}\sigma_{ba}$$ Here $\sigma_{ab}$ is the total reaction cross section for ...
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Built-In Potential (Forward vs Thermal Equilibruim)

According to my book the built-in potential $V_{bi}$ for a PN junction under thermal equiliubrium is: $$V_{bi}= \frac{KT}{q}In(\frac{n_{no}p_{po}}{{n_{i}}^2})$$ where $n_{no}$ and $p_{po}$ are the ...
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Quantum systems with steady states: does a system always approaches the steady state as it evolves?

Say we have a quantum system whose dynamics results in there being a steady state. For example, it may be described by a Linblad master equation with several opposing dissipators. It is obvious that ...
Len's user avatar
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How do powers of ladder operators work in Fock states? [closed]

Hey so I've been working a lot with ladder operators in my physics classes, and got a question: Find $\langle n|\hat{x}^4|n\rangle$ where $\hat{x}=\sqrt{\frac{\hbar}{2m\omega}}(a^\dagger + a)$ and $a^...
Joseph Sciotto's user avatar
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How can one "encode" momentum into the wave-equation of a QM harmonic oscillator? [duplicate]

I am learning about Quantum Mechanics using Griffiths book and after reading the section about the quantum harmonic oscillator, I was left wondering how one can construct a solution to the Schrodinger ...
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How to propagate the wavefunction of a photon in single slit diffraction?

During my undergrad, I remember writing a simulation in which the diffraction patterns which emerge from light passing through a single slit were calculated. This was done, basically, by calculating ...
Gregor Hartl Watters's user avatar
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Understanding the measurement of '"evil" using the GHZ effect

I was reading this interesting article originally published by Quanta Magazine, which tries to explain the GHZ effect in simple terms. The GHZ effect is, in the physicist Sidney Coleman’s words, “...
KDP's user avatar
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In what sense are the eigenfunctions of a Hermitian operator complete? [closed]

I understand that most physicists believe that the eigenfunctions of any Hermitian operator form a complete basis of the Hilbert space. That's why we can use the perturbation method to expand a wave ...
YuanFeng Sheh's user avatar
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What is the difference between tomographically complete and informational complete?

As I understand, a set of effects $\mathcal{E}\subset\mathcal{E}(\mathcal{H})$ are called informational complete if given $\sigma \in \mathcal{T}\mathcal(H)$, $\operatorname{tr}[\sigma E]=0$ for all $...
Godfly666's user avatar
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What is the Taylor series of the expectation value of an observable in quantum mechanics? [closed]

I recently came across a form of the expectation value of an observable, but a Taylor series (I think?) was taken up to second-order: \begin{equation} \langle O\rangle = \langle O\rangle_{C=0} + \...
NikNack's user avatar
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4 answers
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Are the postulates of QM independent of interpretation, or based on Copenhagen?

In particular, I'm talking about the measurement postulate (or at least part of it, I have seen different formulations, here there's one), in which, after measurement of an observable $A$ with ...
agaminon's user avatar
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9 votes
3 answers
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Why do valence electrons not push each other away?

I asked my physics teacher why two electrons come in pairs and not push each other away as you would expect from negative charges. He said that according to the Pauli exclusion principle, there are a ...
Koen de Jong's user avatar
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Prove that a displaced thermal state evolves into a displaced thermal state

Considering the physical model of a harmonic oscillator at frequency $\omega_0$, which interacts with a heat bath at temperature $T$. The relevant Hamiltonians for this model are given as \begin{...
Yashovardhan Jha's user avatar
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Ferromagnetism vs antiferromagnetism

In ferromagnetism the spins align in the same direction, but in antiferromagnetism the spins align in the opposite direction. Both are due to the so-called 'exchange interaction', with a negative ...
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The trace distance between two Gaussian states

If I know two Gaussian states' means and covariance matrixes (both of them are two-mode Gaussian states), how can I compute the trace distance between them?
John James's user avatar
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Overlap between two quantum mechanical states [closed]

I have three questions. This semester my quantum field theory course started and I'm reading Peskin & Schröders book about it right now. They first talk about why relativistic quantum mechanics ...
Gogoman96 X's user avatar
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Can black holes exchange Hawking radiation, avoiding complete evaporation?

I was wondering if it would be possible that, as a black hole radiates its mass as Hawking radiation, another black hole could absorb that radiation and then when the second black hole radiates its ...
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Collapse of wavefunction [duplicate]

Why do the wavefunction always collapse at a single point always when position is measured?
Location's user avatar
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Relation between a diagonal element of a density matrix and the off-diagonal elements in the same row/column [duplicate]

In a density matrix $\rho=(\rho_{ij})$, the diagonal elements $\rho_{jj}$ contains the information about the probability $|\rho_{jj}|^2$ that the $j$-th eigenstate is occupied by the system. Meanwhile,...
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Extending Quantum Treatment of Attentuation Coefficient

I was reading this document to understand the links between the attenuation coefficient and quantum scattering. Consider a beam of number density $\rho$ and velocity $v$ in the z direction. $I = \rho ...
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Constructing a gapped family of Hamiltonians in the trivial paramagnet

Consider the trivial paramagnet, which has the Hamiltonian $$H = - \sum_i \sigma^x_i$$ Now let's say I have two different Hamiltonians $$H_0 = H + 2\sigma^x_{i_0} \qquad H_1 = H + 2\sigma^x_{i_1}$$ ...
pyroscepter's user avatar
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Ccoding for a hamiltonian, ladder operators of a quantum harmonic oscillator [closed]

How do I represent $$a_k ∣n_1 n_2 n_3 ,,,,n_n⟩ = √nk-1 ∣n_1 n_2 n_3 ,,,,n_n⟩$$ and $$a_k^\dagger ∣n_1 n_2 n_3 ,,,,n_n⟩= √nk-1 ∣n_1 n_2 n_3 ,,,,n_n⟩$$ in python(qutip or qiskit preferably) and where ...
saaru darshini's user avatar
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How does the simple description of spin relate to the Dirac equation?

Coming from a chemistry background, spin (the spin 1/2 case at least) is usually introduced in QM by saying there are abstract $\alpha$ and $\beta$ states together with rules for how operators act on ...
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Longitudinal relaxation in NMR - a quantum description?

I'm currently reading Understanding NMR Spectroscopy by J. Keeler and in the section about longitudinal relaxation, he writes that (using $n_i$ for the population of state $i$) the rate of change of $...
FusRoDah's user avatar
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1 vote
2 answers
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Why does the change in probability not depend on the potential for a quantum mechanical particle?

In Griffith's book, the following equation is derived based on schroedinger's equation $\frac \partial {\partial t} \Psi = \frac {i h}{2m} \frac {\partial^2 \Psi} {\partial x^2} - h^{-1}V\Psi$: $$\...
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Why there is steady DC current in a metal under static $E$ field in the presence of Bloch oscillation?

Background: This is a question regarding the Bloch oscillation and the solid state description of shifted Fermi sphere under static electric field. Question: One explanation for a steady current ...
physstudent11's user avatar
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1 answer
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Correlation functions zero for repeated creation or annihilation operators [duplicate]

In the derivation of the damped harmonic oscillator, at some point, see for instance here one has to compute certain correlation functions for the bath of harmonic oscillators in thermal equilibrium. ...
user2820579's user avatar
-1 votes
1 answer
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Is a fermionic boson possible?

We know that bosons need an overall symmetric wavefunction. So is it possible for a boson to have an anti-symmetric spatial wavefunction and an anti-symmetric spin wavefunction? Such that upon ...
Despaxir's user avatar
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3 answers
186 views

Basic doubt in quantum mechanics

Do entities like electrons, which are considered point particles in Classical Mechanics, actually have a definite position at a particular time (irrespective of it can be measured or not)?
Location's user avatar
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Does the Fermi surface drift opposite to electrons in an electric field?

I have encountered somewhat of a paradox when it comes to electrons in an electromagnetic field. I hope someone here knows where the problem lies. Upon minimal coupling of a free classical electron ...
Rooky's user avatar
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General expression for fermionic creation operator subspace

This is perhaps a particular case of the question discussed here. Given a fermionic Fock space $H$ of dimension $2^N$, that is, with $N$ fermionic modes, let $H_n$ be the subspace of states with $n$ ...
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Unitarity of integral transformation from kernel properties

Given a continuous set of bosonic modes $a(x)$, consider an integral transformation of the form $$U a^\dagger(x) U^\dagger = \int dy \ G(x,y)a^\dagger(y). $$ Suppose also that the integral kernel is ...
Phil K.'s user avatar
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1 answer
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Limiting factors in traditional microscopy

I have been researching Entanglement-Enhanced Microscopy, and the overall breakthrough seems to be obtaining a resolution of $1/N$ as opposed to $1/\sqrt N$. This led me to ask what the limiting ...
murtadee hughes's user avatar
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Given a viably physical (isolated), quantum many body Hamiltonian, does an initial state of a superposition of energy eigenstates ever thermalize?

Given a viably physical, quantum many body Hamiltonian of a isolated system, if initially a state is prepared which is a superposition of energy eigenstates in an interval centered at E and E', not at ...
Fibonacci M's user avatar
2 votes
4 answers
151 views

Does Bell’s theorem rule out changing hidden variables?

In the EPR experiment, it is said that there are predictions that are made if there are hidden variables determined by something locally in each particle that results in a correlation in entanglement. ...
Alejandro's user avatar
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Two parameter differential equation solution

I am working on the paper titled "Energetic and entropic effects of bath-induced coherences" (https://arxiv.org/abs/1905.02013)and there is a two parameter differential equation for ...
Meysam Azizi's user avatar
1 vote
1 answer
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Why can't we measure different properties of an electron in accordance with its frequency?

sorry if this is a stupid question but its my first one.. Why cant we just observe and electron in accordance to its frequency. Like during one frequency peak we could observe position, next could be ...
omgcchheeessee's user avatar
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1 answer
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Clarification on bound states: do "locally bound" states exist?

In Griffiths, a state with energy $E$ is said to be "bound" if $$E < \min\left(\lim_{x\to\infty} V(x), \lim_{x\to-\infty} V(x)\right)$$ (i.e. $E$ is less than both of those quantities). ...
Trisztan's user avatar
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1 answer
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Can many-worlds approach testability, if considered in a naively realistic physical context? [closed]

This is more of a philosophical question although it may be acceptable in the context of physics. It concerns Hugh Everett's many worlds interpretation of quantum mechanics. Many popular physicists, ...
DanielFBest's user avatar
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1 answer
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Coordinate-free calculations in bra-ket notation [closed]

I'm interested if bra-ket notation can be used without having to introduce a basis or coordinates in calculations and proofs. For example, could the notation, if need be, extended with some exterior ...
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