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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How is energy defined in QM?

I have been introduced to QM this spring semester. One thing that I couldn't understand is that how do they define the energy of an electron. For example while solving "Particle in a box" ...
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Entangled particles and the Andromeda paradox experiment

I know there are other questions linking the two subjects. I am not asking about an explanation, rather I am curious whether an experiment would be possible. To explain the experiment let's start with ...
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Divergence of the Berry connection

Given the Berry connection \begin{equation} \boldsymbol{\mathcal{A}}(\mathbf{R}) = i \langle u(\mathbf{R}) | \nabla_\mathbf{R} | u(\mathbf{R}) \rangle, \end{equation} the Berry curvature can be ...
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Showing the Variance of an observable in a determinate state is always zero

I am working through Introduction to Quantum Mechanics by David J. Griffiths, and part 3.2.2 shows that the standard deviation of an obervable, $Q$, is always $0$ but I do not understand the steps ...
cookiecainsy's user avatar
6 votes
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Entropy during spontaneous symmetry breaking

Spontaneous symmetry breaking (SSB) occurs when the state of a system possesses less symmetry than the underlying laws governing it. This raises the question: What happens to the entropy of the system ...
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Square Integrability of spherical symmetric wave

In my class we were discussing some wave equation for a spherical symmetric wave $u(t,r)$ and my professor investigated the behaviour of the solutions asymptotics $r \rightarrow \infty$. The solution ...
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Usage in the Clebsch-Gordan (CG) coefficients' recursive relation

In Sakurai's Modern Quantum Mechanics, its 3.8.39 is \begin{aligned}\sqrt{(j\mp m)(j\pm m+1)}\langle j_1j_2;m_1m_2|j_1j_2;j,m\pm1 \rangle \\=\sqrt{(j_1\mp m_1+1)(j_1\pm m_1)}\langle j_1j_2;m_1\mp1,...
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Effects of measurement on the entropy in quantum mechanics

How does measurement in quantum mechanics (QM) impact the system's entropy? The measurement process in QM is considered time-irreversible. Are there principles akin to the second law of thermodynamics ...
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Is it possible to model unidirectional evolution of an atom-photon system using the Schrodinger equation?

The physical system I'm imagining is pretty simple: suppose there's an atom in free space with three states $|g_0\rangle, |g_1\rangle, |e\rangle$ initialized to some superposition of $|g_0\rangle$ and ...
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Lifting Projective representations [migrated]

D. J. Simms in his book "Lie groups and quantum mechanics" (page 9) says that: any representation of $\sigma$ of $\tilde{G}$ (the simplgy connected covering group of the Lie group) in $U(H)$ ...
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Question about impurity scattering of multiband Hamiltonians in $T$-matrix approximation

Imagine, we have a 2-by-2 Hamiltonian: $$ H = H_0+H_{imp}. $$ The impurity Hamiltonian $H_{imp}$ is $$H_{imp}=u_{imp}I_2\sum_{r_{imp}}\delta(\vec r - \vec r_{imp}).$$ $I_2$ is identity matrix of order ...
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How to prove that the spin operator commutes with the position operator? [duplicate]

In the lecture notes on Quantum Mechanics I'm reading, the author claims that the position operator $\hat{q}$, the square spin operator $\hat{s}^2$ and the spin operator component $\hat{s}_0$ (in a ...
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Quantum oracle for boolean function

As a math student, I am doing some quantum computing. In the course notes of Ronald de Wolf, he says that any Boolean function $$f:\{0,1\}^n\to\{0,1\}^m$$ can be made into a unitary operation that ...
student's user avatar
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Tightly-focusing a single photon

I'm curious about the feasibility, both theoretically and experimentally, of tightly focusing (or spatially trapping) a single photon to guarantee its precise targeting. If it’s possible, isn’t it ...
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Unusual example of Compton Scattering (+Four-momentum approach, +nonrelativistic) [closed]

An electron of kinetic energy $k=100 keV$ (first note, doesn't this mean that its energy is much lower than $0.511 MeV$, and thus that it is a nonrelativistic electron we are dealing with?), collides ...
CogitoErgoCogito's user avatar
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Lindblad evolution as continuum limit of a discrete process coupling system and environment

I have trouble understanding the derivation of the Lindblad evolution in terms of the time evolution under a Hamiltonian $H$ in a system-environment Hilbert space $H_S\otimes H_E$, where we trace out ...
Andi Bauer's user avatar
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Rotational quantum states for atoms

It is well-established that molecules possess rotational and vibrational quantum states, due to molecular symmetries, in addition to electronic states. In contrast, it is generally accepted that atoms ...
Omid's user avatar
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Positronium radius more than expected

I am trying to derive the basic properties of positronium. Usually it is stated that we can just set reduced mass of hydrogen atom as $\dfrac{1}{2}m_e$ and obtain: \begin{equation} r_n=\dfrac{8\pi\...
Aslan Monahov's user avatar
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Limit for big system size of Fokker-Planck eigenfunctions

I am learning how to use diagonalization methods applied to Fokker-Planck equations with Gardiner's book and these notes. The idea is to find the probability density, $ P[X_t\in[x,x+dx]]=\rho_t \, dx$,...
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Does the density matrix still holds for infinite subsytems?

Consider a maximally mixed state composed of $n$ equal qubits. Its density matrix is then:$$\hat{\rho}^{(n)}=\hat{\rho}^{\otimes n}.$$ The eignevalues of such a matrix, $\lambda$ will all be equal (...
Oscarcillo's user avatar
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3 answers
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Relation between classical probability and quantum probability formulae

Assuming superposition state $$ \Psi = C_1 \psi_1 + C_2 \psi_2 $$ ,one can write the expectation value $\langle A \rangle$ of a physical magnitude A as follows $$ \langle A\rangle = P_1 \langle A\...
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If $H$ anniliates a state, must $Q$ and $Q^\dagger$ also annihilate the state?

Suppose we have a a Hamiltonian, $H$. And suppose also we have some operator $Q$ such that $\{Q, Q^{\dagger}\} = H$, and $Q^2 = 0$. If we find a state $|\psi \rangle$ such that $Q|\psi \rangle = Q^{\...
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Why are $j=0,\frac{1}{2},1,\frac{3}{2},\ldots$ representations of $SU(2)$ algebra irreducible? [migrated]

In quantum mechanics, we construct all the representations of the $SU(2)$ algebra $$[J_j,J_k]=i\varepsilon_{jk\ell}J_\ell$$ in the $|j,m\rangle$ basis. The allowed values of $j$ turn out to be $$j=0,\...
Solidification's user avatar
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Trying to learn input-output formalism: 2-photon Fock state entering a cavity

I really don't understand the input-output formalism. I've gone through the 1985 paper, and I get completely lost when the following formula is written: $$b_{out}(t)-b_{in}(t) = \sqrt{\gamma} c(t)$$ ...
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Uncertainty principle for incompatible observables whose probability distributions lack well-defined moments

The Heisenberg uncertainty principle states that the product of standard deviations (or variances) for incompatible observables has a non-zero lower bound (with a zero lower bound reserved for ...
Omid's user avatar
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The relative phase of photons in two-photon absorption

In two-photon absorption (TPA), the relative polarization of the two photons about to be absorbed simultaneously by an atom is crucial in determining the TPA rate. However, there is a lack of ...
Omid's user avatar
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Nature of a superposition of states: is it true or only theoretical?

For quantum mechanics, a certain property of a subatomic particle, e.g. the spin of an electron, which can be either up or down, is a "superposition of states," and one of the two conditions,...
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Can we create a space in which density of all electromagnetic fields is 0?

so i was just thinking that may be the reason of that we cannot measure a quantum particle position and velocity may be because continuously it's being hit by electromagnetic radiation and since we ...
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Can we get quasiprobability distributions other than $P,Q,W$ from generalised characteristic functions?

It's a standard result that the three well-known quasiprobability distributions can all be expressed in terms of the "$s$-ordered characteristic functions" as $$ W(\alpha) = \int\frac{d^2\...
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Why does quantum random walk show ballistic transport?

For the topic of quantum random walk, a simple example is considering a 1D lattice fermionic model, expressed as $H = \sum_{i} c_i^\dagger c_{i+1} + h.c.$ Assuming there is one fermion located at the $...
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Can we prevent the Higgs field interaction with particles? [closed]

if not why? is it possible in future? Because if it is possible there may be chance of more advance invention
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Planck's quantum explanation of black body radiators

Oscillators in a black body (electrons) can only have energy equal to $E = nhf$ ie it is a linear relationship. so if an electron drops from energy level $n$ to a lower energy (jumping 1, 2,3 ... ...
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Expectation Value Involving $s$-Wave Solutions to Central Potential

I previously posted a question regarding the expectation value described below, but it was closed because the question was not developed enough. Since I was given the option to delete it, I deleted it;...
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How can a QFT field act on particle states in Fock space?

Recently I asked a question that was considered a duplicate. However I felt that the related question didn't answer my doubts. After a bit of pondering I have realized the core of my discomfort with ...
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What does it mean for classical mechanics to be based on the category of sets?

It is quite common[1][2] in the study of physics in the context of category theory to say that one of the fundamental difference between classical mechanics and quantum mechanics is that classical ...
Slereah's user avatar
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2 votes
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The limit of time evolution operator

Through reading Nenciu's rigorous proof on the Adiabatic Theorem and Gell-Mann-Low Theorem, I found: Since the limit $t_0\to-\infty$ does not exist for $U(t,t_0,\epsilon)$, in order to make use of ...
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Single Photon Interference and the Hong-Ou-Mandel (HOM) Effect in an Interferometer

Reading on the Hong-Ou-Mandel (HOM) effect, I came to wonder how exactly we can be certain that interference that occurs in apparatuses such as a Michelson interferometer and Mach-Zehnder ...
OneStrangeQuark's user avatar
3 votes
1 answer
72 views

Why are the angular momentum raising and lowering operator coefficients real?

I had a homework problem where I had to find the coefficients for the angular momentum raising and lowering operators. I know the answer is supposed to be $\sqrt{l(l+1)-m(m\pm1)}$. I have figured out ...
toomanyfeet's user avatar
4 votes
0 answers
106 views

How to interpret QFT fields (in relation with QM)? [duplicate]

In QM we deal with the Schrödinger equation:1 $$i\frac{\partial}{\partial t}\psi = H \psi$$ the wave function $\psi(x)$ is the main object of interest: it can be interpreted as a scalar field, in the ...
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Why we cannot transfer information using a spin entangled singlet? [duplicate]

In QM and QE effects an entangled particle pair is called also a singlet with some properties of the two particles like spin, non-locally correlated. However, there is no transfer of information ...
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Deducing the ground state from a known first excited state

I am studying Schrodinger equation with a potential of hyberpolic functions. $$ H \psi = - \psi''(x) + \Big[1-\frac{12}{1+b \cosh{(2x)}} + \frac{15\,(1-b^2)}{[1+b \cosh{(2x)}]^2}\Big]\psi(x) $$ The ...
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Experimental implications of unitarity [duplicate]

I have two questions with regards to unitarity: To which extent it has been verified experimentally that quantum systems evolve in a unitary way when dealing with unbounded Hamiltonians? Let us ...
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What is the distinction between a ket and a state in quantum mechanics?

Sorry if this has been asked before in some manner, but I'm just a bit confused about the distinction between a state $\alpha$ and its ket $|\alpha\rangle$. I was recently told that a state $\alpha$ ...
Pedro Hablespanyos's user avatar
2 votes
1 answer
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Probability distribution for the momentum of a quantum harmonic oscillator

I was wondering if anyone could point me towards the analytical solution for the probability distribution for the momentum of a quantum harmonic oscillator in the canonical ensemble. I've come across ...
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A quantum machine that works unitarily and doesn't produce heat

For decades since my physics master's I daydreamed about machines that work on a quantum level unitarily. The reason I found it interesting was because I knew that unitaries map pure states to pure ...
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Intuitive intermolecular explanation required for why same force applied farther from a hinge causes larger acceleration than if applied closer?

Intuitive intermolecular explanation required for why same force applied farther from a hinge causes larger angular acceleration than if applied closer? No math or equation required. This question is ...
Tough questions's user avatar
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1 answer
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Are the SHO's ladder operators induced from a Lie group action?

Consider a quantum system with a hamiltonian $\hat{H}$, which is invariant under the action of a lie group $G$, meaning we have a unitary representation of $G$, $\hat{U}(g)$, in Hilbert space, and $\...
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Question about quantum mechanics wave equation deduced by mechanics-optics analogy [closed]

I have a question about quantum mechanics wave equation deduced by the analogy between eikonal equation and fermat least principle (in optics) with, respectively, hamilton jacobi equation and ...
user273366's user avatar
1 vote
1 answer
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What will be wave function after application of operator?

In the mathematical treatment of quantum mechanics, we have a wave function ($ψ$) that helps us to know the different information (like position, velocity, energy, etc.). To measure such a quantity we ...
roshannepal_x's user avatar
5 votes
1 answer
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A theoretical issue in the mathematical description of the Aharonov-Bohm experiment

Mathematically viewing, the Aharonov-Bohm experiment shows that the magnetic field creates a connection with a nonzero holonomy on a multiply-connected domain. This means that there isn't a state ...
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