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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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Schroedinger equation with value of wave function in polar coordinates?

I'm trying to get a better sense of what causes an increase in the magnitude and phase of the wave function at a given point. Is there a way to rewrite the schroedinger equation such that it ...
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Quantum Master Equation for Damped Harmonic Oscillator

In the book, Statistical Methods in Quantum Optics Volume 1, while writing the master equation for the damped harmonic oscillator system, I am not able to understand how the system operators S1 and S2 ...
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Schrodinger's Kersplatt [closed]

Consider the following thought experiment, based on Schrodinger's cat. Electron 1 is prepared in a superposition of spin up and down Electron 2 is prepared in spin down A box, isolated from the rest ...
Peter A's user avatar
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Question regarding the half Harmonic Oscillator

In the normal Quantum Harmonic Oscillator(QHO), we normally use the operator method(because it's to elegant), but I recently discovered the problem in Griffiths(prob 2.42) where they asked the same ...
Charu _Bamble's user avatar
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Basic confusion about evolution of wave function of a free particle

I am going through Griffith's introduction to quantum mechanics. An example for a free particle is given where $$\Psi(x,0) = \begin {cases}A \quad \text{if } x\in [-a,a]\\ 0\quad \text{otherwise}\end{...
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Is magnetism an intrinsic property of matter like electric charge

So here’s what I understand so far A moving charge produces a magnetic field but I don’t know why(maybe something to do with special relativity but that doesn’t really explain why a single charge ...
the mega ruler's user avatar
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Are projective representiations of a Lie group a representation of the semi-direct product of the group with $U(1)$ if the norm is preserved?

Let's say we have a function $f(x_{\mu},t)$ that transforms under the action of an $N$-parameter group $G(a_{\nu})$. Then a projective representation of $G(a_\nu)$ in the $f(x_\mu,t)$ basis would ...
Ilya Iakoub's user avatar
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Quantum Confinement

I have been reading about quantum confinement, and I came across two statements. "Quantum confinement occurs when the dimension of the confining region is comparable to the wavelength of the ...
Udit Chauhan's user avatar
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Constant of Motion in Quantum Mechanics for explicit time-dependent Operators

I was studying constants of motion in quantum mechanics, and at first, I don't understand the condition to be a constant of motion. Generally, the temporal variation of an operator $A$ is given by the ...
QuantumBrachistochrone's user avatar
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About how to calculate observables in QMC with complex weights

I'm rewriting a DQMC algorithm following Werner, P., Oka, T., & Millis, A. J. (2009). Diagrammatic Monte Carlo simulation of nonequilibrium systems. Physical Review B, 79(3), 035320. In this ...
pter26's user avatar
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Relationship between drift velocity and processor speed

Does having higher drift velocity for electrons lead to faster processors? If yes, how? The speed of processors is higher or lower depending on the speed of the on off states, i.e. the speed of the ...
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Why do we assume that all electrons in an atom are in $m_s$ eigenstates, and that each one is in a simultaneous $m_l$ and $m_s$ eigenstate?

I have already read the following discussions and would like to point out that my question goes in a different direction: If superposition is possible in QM, why do we often assume systems are already ...
UVcatastrophe's user avatar
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How to write single particle potential operator $U$ using field operators [closed]

I want to derive the field operator form of single-particle potential operator, so that: \begin{equation} U = \sum_{ij} u_{ij} a_i^\dagger a_j = \int d^3x\; u(\vec{x})\psi^\dagger (\vec{x}) \psi(\vec{...
Killaduu's user avatar
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How important are purely imaginary finite action solutions for first order instanton contributions?

I am working on a physics problem where I have to calculate instanton contributions for a non-relativistic Hamiltonian $$H=-\frac{1}{2}\frac{d^2}{dx^2}+\frac{1}{2}x^2+\frac{1}{6}g^2x^6 \tag 1$$ for ...
Young Plato's user avatar
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How can you have position basis and energy basis? [duplicate]

In Quantum Mechanics, my understanding is that we have a Hilbert space. If we to model a particle in space we consider the space defined by the basis $$|x\rangle$$ for each $x \in \mathbb{R}$ We then ...
Charlie Thomas's user avatar
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Calibration Method used in Compton Scattering project [closed]

In a project in which it studies experimentally the angle dependency of the energy of scattered radiation. The scatterer used in the experiment is an aluminum plate. The equipment can change the ...
Tansu A's user avatar
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Scattering by point potentials

Suppose we consider the quantum scattering of two particles. The interaction Hamiltonian is given by: $$H = -\Delta_{\vec{x}}-\Delta_{\vec{y}} +V(x-y)$$ where $V$ is the interaction potential between ...
JustWannaKnow's user avatar
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Tunneling probability dependence from the initial velocity (approching 1 for high velocity)? [closed]

Imagining high velocity e.g. electrons, probability of crossing a barrier naively should approach 1. How to calculate it with Schrödinger equation? Is there some available experimental data? Searching ...
Jarek Duda's user avatar
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Current Inside the Depletion Region Forward Biased PN Junction

For a forward biased PN junction, we assume the hole and electron currents are constant inside the depletion region when there is no generation or recombination in the depletion region (shown from the ...
Abe 's user avatar
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Partition function expression from a discrete Hubbard-Stratonovich transformation

$\DeclareMathOperator{tr}{tr}$ This question is about a very specific (but very mysterious to me) detail. In some quantum Monte Carlo methods such as determinant QMC, the partition function $Z = \tr e^...
Banach space fan's user avatar
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How to find a normalized state vector that is orthogonal to a given state? [closed]

Consider state: $$ |\psi\rangle=\frac{3}{\sqrt{34}}|+\rangle+\frac{5i}{\sqrt{34}}|-\rangle. $$ The problem is to find a normalized state that is orthogonal to $|\psi\rangle$. Here is what I tried, but ...
LoopGod's user avatar
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0 answers
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Quantum Mechanics calculating the $V(x)$ [closed]

The ground state (apart from normalization) of a particle of unit mass moving in a one-dimensional potential $V(x)$ is $\exp(-x²/2) \cosh(√2x).$ What is The potential $V(x)$, in suitable units so that ...
Sayak's user avatar
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Why Normalise by $h$ in the Partition Function for Classical Harmonic Oscillator?

I was wondering if anyone could explain the reasoning behind the $h$ normalization constant when calculating the partition function for a classical harmonic oscillator. I know that the partition ...
392or385's user avatar
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Is Paramagnetic Current Density Operator Hermite?

When free electrons are exposed to the electromagnetic field, the current density operator has a modification, which can be divided into so-called paramagnetic and diamagnetic parts: \begin{align} j_p&...
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On the choice of observables in linear response theory

For linear response theory I need two observables. The idea is to see how the change in one observable changes the other under weak perturbations in equilibrium state. Suppose I want to see the change ...
Rafi Ullah's user avatar
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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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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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1 answer
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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
1 vote
1 answer
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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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1 answer
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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 ...
Abe 's user avatar
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1 answer
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Quantum systems with steady states: does a system always approach 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 ...
Mantabit's user avatar
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2 answers
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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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1 answer
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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
1 vote
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63 views

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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3 votes
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
1 vote
1 answer
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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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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
1 vote
0 answers
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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?
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