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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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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The possibility of having two objects present together at the same place and time?

Can an electron exist simultaneously in the same place and time? Although an atom is mostly empty space, attempting to penetrate this vacuum would result in collision with the electron, as it occupies ...
Muhhamedbinghazi's user avatar
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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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For the Schroedinger Equation, can you find the wavefunction of a system from the energy? [closed]

For example, the Schroedinger equation may be solved for the Hydrogen atom. We know that the energy is -13.6 eV for the ground state, and so I was wondering if we could work backwards to solve for the ...
lzzard's user avatar
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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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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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Kindly help regarding the Hamiltonians [closed]

Suppose we have the following Hamiltonian: $$\begin{aligned} H= & \Delta_a a^{\dagger} a+\Delta_b b^{\dagger} b+\Delta_c c^{\dagger} c+\Omega\left(c^{\dagger}+c\right)+J_1\left(a^{\dagger} c+c^{\...
Bhaskar Kumar's user avatar
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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
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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
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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 ...
Noumeno's user avatar
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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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Problem on Heisenberg group [closed]

Show that the set in $R^3$ with the group law: $$(s, x, y) ∗ (s_0 , x_0 , y_0 ) = (s + s_0 + xy_0 , x + x_0 , y + y_0 )$$ is isomorphic to the Heisenberg group with group law : $$(s, x, y) ∗ (s_0 , ...
flyredeagle's user avatar
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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 ...
Mohamed S. Mahdi's user avatar
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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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Unitary of the Schrödinger equation evolution [closed]

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 ...
Yair's user avatar
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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
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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 ...
aQuarkyName's user avatar
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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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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 $\...
roymend's user avatar
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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
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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
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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 ...
mma's user avatar
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Head-on collision of $\rm N_2$ and $\rm CO_2$ molecules [duplicate]

Consider a standing sound wave formed in the air in conditions close to standard pressure and temperature in the antinode region. On the molecular level, it will involve multiple collisions of air ...
Stan Tarka's user avatar
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2 answers
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Can it be disproven that an electron is a wave packet of photons? [closed]

When an electron collides with a positron, both are destroyed and pure energy in the form of photons is released. It seems then that electrons are composed of photons, if photons were released on ...
EngineeringMind's user avatar
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Phase shift in hard sphere scattering

Consider scattering towards a hard sphere with radius a and potential (Assume ka=1): $$ V(r) =\begin{cases} \infty , &r<a\\ 0 , &r>a \\ \end{cases} $$ So first I ...
ilra's user avatar
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What is the difference between local operations and global operations for quantum systems?

When I hear people talk about qubit operations, they usually make a distinction between local and multi-qubit (global) operations. I understand what they mean intuitively (the local operations act on ...
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Coulomb scattering amplitude in terms of phase shifts

I am reading Introductory Nuclear Physics by Wong. In Appendix B-2, he shows that the Coulomb scattering amplitude is given by $$ f^c(\theta) = -\frac{\gamma}{2k\sin^2(\theta/2)} e^{i[\gamma\ln(\sin^2\...
MarcosMFlores's user avatar
3 votes
1 answer
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Why does this not break the security of quantum teleportation

I am taking an course on quantum mechanics, and we have just encountered the quantum teleportation protocol that allows for the transfer of one qubit from Alice to Bob. I think I have a way for Eve to ...
Jack's user avatar
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What happens when two photon of same polarization enters in the polarizing beam-splitter(PBS)?

It is well established that if two photons of the same polarization, identical wavelength, phase, and spatial distribution of wavefunction enter a non-polarizing beam splitter (N-PBS), they exhibit ...
Kanad Sengupta's user avatar
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0 answers
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Vacuum-generator using Casimir effect? [duplicate]

Is the Casimir-effect viewed in microscopic timestamps a static or a periodic force? In my view the Casimir effect (if periodic pushing of the metal plates through the larger random fluctuations ...
JoA's user avatar
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5 votes
2 answers
180 views

Energy levels of a translating quantum harmonic oscillator

It is well known that the energy levels $$ E_n = \hbar \omega\left(n+\frac{1}{2}\right) $$ of the quantum harmonic oscillator verify the eigenvalue problem $$ \hat{H}|\psi_n\rangle = E_n |\psi_n \...
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-1 votes
1 answer
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Time reversal in momentum space [closed]

So I'm trying to find the wave function in momentum representation for the state $\hat{T}|\psi⟩$, where $\hat{T}$ is the time-reversal operator. First, we know that the time reversal operator acts on ...
ilra's user avatar
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Self-energy of a fermion system with critical hybridization?

Consider the following Hamiltonian, with two species of fermions ($c$ and $f$) and only inter-species local interactions: $$ H = \sum_k \epsilon_k c_k^\dagger c_k + \sum_q \varepsilon_q f_q^\dagger ...
dumbpotato's user avatar
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1 answer
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"Derivation" of group velocity and "sharply" peaked wave functions

I was reading BH Bransden's chapter on wave packets and he derives the group velocity expression taking into account that: $$ \psi (x,t)=\int e^{i[p_{x}x-E(p_{x})t]/ \hbar} \phi (p_{x}) dp_{x} $$ ...
Álvaro's user avatar
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2 answers
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What does $f(x)$ satisfies the given equation means?

In problem 2.1 part c of Introduction to Quantum Mechanics, 3rd ed. by Griffiths and Schroeter, they ask the reader to prove that if the potential is an even function of $x$, then if $\psi(x)$ ...
GedankenExperimentalist's user avatar
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Ehrenfest Theorem For $s$-Waves of Central Potential [closed]

Consider a central potential $V(r)$ and an $s$-wave wavefunction $\psi = \frac{1}{\sqrt{4\pi}}\phi(r)$ where the coefficient is just the spherical harmonic $Y_{00}$. This wavefunction is an eigenstate ...
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What is meant by a "critical system"?

I see "critical system" being used all the time. For example: Excellent candidates for this approach are systems exhibiting phase transitions. At the critical point of a phase transition, ...
NikNack's user avatar
2 votes
2 answers
54 views

Spin-orbit interaction and retarded potential

Can anyone explain to me why, when the spin-orbit interaction is a relativistic effect, the Coulomb potential is then used in calculating the hydrogen energy levels, rather than the retarded potential?...
dgwp's user avatar
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A possible Theory of Everything and I need your thoughts [closed]

For over 20 years I've slowly pieced together this simplified idea of a Theory of Everything and now I've gotten all the pieces put together. My main goal is to get the idea out there for scientists ...
Ronald Rothrock's user avatar
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1 answer
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Square of the density operator for a mixed state [duplicate]

Consider a density operator $\hat{\rho}$ for a mixed state defined by $$\hat{\rho} = \sum_k p_k |\psi_k\rangle \langle\psi_k|$$ Here $p_k$ is the probability of finding the $k$th system of the ...
omegadot's user avatar
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3 votes
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Why are these unbounded operators (essentially) self-adjoint?

Can anyone provide exact mathematical reasoning as to why the following fundamental unbounded symmetric operators are essentially self-adjoint? I.e. on, their natural domains, they admit a unique ...
SiOn's user avatar
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What should be minimum width of slit for interference pattern to occur in a single slit experiment? [duplicate]

When two slits produce an interference pattern, and one slit is closed, then the interference pattern disappears. Why? As one-slit interference is still possible. What should be the measurements of ...
Odal's user avatar
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Dual nature of matter on macroscopic bodies like that of humans or anything

if matter has a dual nature and everything is made up of matter then why do macroscopic bodies like humans or trees or a cars is not showing wave motion like why are they static and not moving like a ...
Anugrah Sengar's user avatar
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2 answers
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Are Hermitian operators Hermitian in any basis? [closed]

Given a Hilbert space and a Hermitian operator defined on it, will the operator exhibit Hermiticity in any basis used to span the space? My thought on this is that this must be the case, after all, if ...
Albertus Magnus's user avatar
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3 answers
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What happens if two people have different knowledge about a state in a quantum mechanical system?

Let’s say I measure the spin of an electron, but I don’t tell you what it is and you don’t measure it yourself. Does that change the wave function for you or does it remain the same either way? If it ...
Name's user avatar
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Scattering amplitude in first Born approximation [closed]

I'm just trying to understand the solution to this problem but can't really get what happened in the last row! How does the integral become like this?
ilra's user avatar
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How to compute the hopping matrix considering the change of multiple states?

My question is quite simple, but I couldn't find the answer anywhere. Hubbard Models usually have a hopping term as follow: $$H_{hop} = -t \sum_{<i,j>} \left( c^{\dagger}_{j} c_{i} + c^{\dagger}...
C. R. L.'s user avatar
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Trace properties of anti-commuting matrices [closed]

Suppose I have a finite dimensional complex inner product space $V$ and matrices $A_{1},...,A_{n}$. By $A^{*}_{i}$ I mean the adjoint matrix of $A_{i}$. Assume that these matrices satisfy anti-...
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