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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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Partition function in the non-interacting limit

Let's consider the partition function $$Z(\lambda)=Tr (e^{-\beta H})=Tr (e^{-\beta (H_1+\lambda H_2)})$$ for a quantum system with the Hamiltonian $H=H_1+\lambda H_2$ where $H_1$ is the free part of ...
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Why this is classical correlation and not full (classical + quantum) correlation?

Let a quantum system be given which has two subsystems $A$ and $B$ so that the Hilbert space decomposes $\mathscr{H}\simeq \mathscr{H}_A\otimes \mathscr{H}_B$. If the state of the system is $\rho$, ...
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When do you use Quantum Mechanics? [duplicate]

Given a problem, how does one know whether to use quantum mechanics or classical mechanics? Take for example electron scattering from a nucleus. The electrons are given a wavefunction in this case. ...
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Solution of the coupled non-linear oscillators by using perturbation theory [closed]

The integration shown here, $$∫_{-\infty}^{+∞}x^r\mathrm{Exp}[−x^2]\mathrm{H_n}^2[x]\mathrm{d}x,$$ appears when we try to calculate the spectrum of the perturbed non-linear oscillators by using ...
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Commuting Operators in Integral

If I have $$ \hat{H} = \int d^3r \hat{\psi}^\dagger(\textbf{r}) H_1(\textbf{r})\hat{\psi}(\textbf{r})$$ How does commutation work with the $\hat{\psi}(\textbf{r})$ with the $H_1(\textbf{r})$? I know ...
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Gaining intuition about summing over random basis vectors in random matrix theory

I'm currently reading the following reference on eigenstate thermalization and chaos in quantum mechanics: https://arxiv.org/abs/1509.06411 I'm confused by a derivation that I think is very important ...
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Understanding the statement of the bandwidth theorem

I know that the Bandwidth Theorem (BT) and the Heisenberg Uncertainty Principle (HUP) are basically the same thing, and stem from the fact that for operators $A,B$, we have: $$\Delta A \Delta B \geq \...
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Perfectly distinguishable states are mutually orthogonal

$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}$ Let $H$ be a Hilbert space. We call states $\ket{\psi_1}, \...
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Can we use the Pascal triangle as an aid to construct superpositions of wavefunctions corresponding to $n$ electron spins?

Suppose we have n electrons and want to construct the wavefunction corresponding to the spins of the electrons. Can we construct this wavefunction (in the $(s_1,s_2,s_3 ... s_n)$ representation, so ...
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Calculation of path integral in QFT

I am studing QFT using the text book of Srednicki's. And I am stuck on one of calculations of the integrals in his book. Consider a harmonic oscillator with hamiltonian: We can write the following ...
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Where is the line between Quantum and Relativity?

Its often said QM is for the very small and GR for the very large. This brings to mind that there should be some limit at which one starts to apply and the other stops. Now I know there are more ...
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Why do neutron stars with more mass have smaller volume?

I know about Heisenberg uncertainty which makes more localized neutrons have a wider range of undefined momentum, and Pauli exclusion principle which prohibit neutrons from getting too close or "...
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Classical mechanics in coadjoint orbits

We know that coadjoint orbits are symplectic manifolds, and they can be used to find unitary representations of Lie groups and stuff, and it's also related to quantization. However, is it true that ...
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Symmetries of a differential equation, its solutions and hydrogen atom

A symmetry of a differential equation need not be shared by its solutions. However, under that symmetry, the one solution goes to another. For example, consider the time-independent Schrodinger ...
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What's the outcome of measuring photons that are entangled in phi + and - states in RL, HV and +- basis? [closed]

Sorry for my bad english! Please, I'm trying to understand a delayed choice entanglement swapping and I'm having trouble at understanding the outcomes of measuring photons that are enangled in phi + ...
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Classical angular momentum components are numbers. Can they be generators of some symmetry group?

In Quantum Mechanics (QM), angular momentum turn out to be the generator of rotational symmetry. This is trivial to see because in QM, angular momenta are defined by the commutation relations $$[J_j,...
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Ehrenfest theorem and the distinction between moment ordinal 1 and moment ordinal 2 of the measured probability distributions

The proof of the statement of Ehrenfest theorem in the Schrodinger picture does not depend on the state vector. However, Wikipedia claims that: for states that are highly localized in space, the ...
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Why is energy proportional to light's frequency? [duplicate]

I can appreciate that light can be quantised into photons, but I'm having a bit of difficulty understanding Planck's formula $$E=hf$$ Perhaps I am lacking intuition, but I don't really see why higher ...
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Infinite vs Finite dimensional Hilbert space

Let us consider an electron in an infinite square well. As we know that the electron has a spin=$1/2$ . The spin operator ($z$-direction) has two eigenvectors which span the vector space. But if we ...
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What exactly is $\langle x |$?

It's a linear functional, but what exactly does it do? It maps a wavefunction $|\psi \rangle$ to an element of $\mathbb C$, but what.. exactly does that mean? I know heuristically it maps $\psi$ to ...
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How does the hydrogen atom actually “look like”? [duplicate]

When deriving the solutions for the "simple" quantum mechanical hydrogen problem, one normally uses spherical coordinates $(r,\theta,\phi)$, since the problem has rotational symmetry. The solution has ...
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Do superposition entangled Qubits need to be collapsed at the same time to reveal the same state? [closed]

Or can one set of entangled Qubits be collapsed first, with the second set collapsed later and achieve the same values?
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Do qubits need to be in superposition to be entangled? [closed]

Do qubits need to be in superposition to be entangled? Put another way, can qubits be entangled but not in superposition?
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Good /not good quantum numbers in spin-orbit coupling

Given that the Hamiltonian associated with the spin-orbit interaction can be expressed in terms of the total orbital angular momentum and total spin operators as: $$ H_{SO} = -\frac{e}{2m_e ^2 c^2} \...
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Why is wave-function collapse still being taught in quantum mechanics? [closed]

I don't really understand why wave-function collapse is still being taught while we seem to have better interpretations of QM available nowadays. During the early development of quantum mechanics the ...
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Description of quantum state of entangled photons after polarizer

I'm wondering if anyone can help me understand how a polarizer changes the quantum state of two polarization-entangled photons. I haven't found a clear description in the literature. Suppose you have ...
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What depicts the logo of Physics StackExchange? [migrated]

I am just interested. I guess there is a relation to magnetic fiels or quantum physics but I have no clear idea of it.
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1answer
81 views

Number of photons in range of frequencies

I was trying to calculate the number of photons emitted by a light of constant power $P$ between frequencies $\nu_1$ and $\nu_2$. I have already checked this question but the reply marked as correct ...
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Entropy, time reversibility, and the uncertainty principle

I had a coworker bring up time reversibility during a lunchtime conversation the other day and how physical systems would behave. Sparing the unimportant details of the conversation, his position was ...
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Chemical bonding based on hybridisation model [migrated]

A snippet from a textbook: 'Therefore, the hybridization model predicts that an sp-hybridized carbon atom is more electronegative than an sp3-hybridized carbon atom. Evidence for this effect is that ...
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Superposition principle forbids quantisation?

Apparently bound states in quantum mechanics require energy states to be discrete. That means energy in such systems is quantized, right? However, say that we have a superposition of energy ...
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Rotating wave approximation

What is meant by counter rotating terms seen in the derivation of Jaynes Cummings model and what influence does it make if they are not neglected?
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Are quantum mechanical orbits specified uniquely by a Hamiltonian and initial state?

EDIT: This is completely wrong, don't bother reading. Consider a finite dimensional quantum mechanical system, say an $N$-qubit system so that $\text{dim}(\mathcal{H})=2^{N}$. Let's prepare our ...
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Are all superposition principles related?

Are all superposition principles related? Is there a relationship between the microscopic superposition principle and the macroscopic superposition principle? Does the microscopic one lend to the ...
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What is energy in quantum mechanics?

Is it wrong to say energy is the expectation value of Hamiltonian? Or should I say energy is the eigenvalue of Hamiltonian?
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Green's function for infinite square well

The Green's function can be given in terms of left and right solutions. $G(x,x';k) = \frac{1}{W}\left(\Psi_{L}(x_{<})\Psi_{R}(x_{>})\right)$ But I don't understand how to determine these left ...
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So is quantum entanglement actually FTL “communication” or is it mundane pre-determination?

I have to say right off the bat, I'm a little frustrated that there seem to be very contradictory answers about this, at least to a layman like me. If two particles are entangled and you separate them ...
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Clebsch-Gordan coefficients for more than 2 particles

I need to couple arbitrary spins together and need Clebsch-Gordan coefficients for them. This should be just coupling the last two particles, then couple the next until the first particle is coupled. ...
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Time reversal of a QM Hamiltonian

I'm interested in the time reversal properties of a term in the non-relativistic QM Hamiltonian proportional (up to a true scalar) to $$ H \propto (\vec S_1 \times \vec S_2) \cdot \vec L $$ The ...
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Accuracy of Heisenberg Uncertainty Principle for estimating ground state energy of particle in potential well

I've understood the assumptions and logic behind the 'proof' that the ground state of a particle in an infinite potential well has a non-zero energy using the Heisenberg Uncertainty Principle. ...
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Freedom of choice of phase for operator in QM

For simplicity, I consider a 2 dimensional Hilbert space. In Q.M we have a freedom of choice for a global phase of a wavefunction. But here I am interested in the freedom of choice we could have for ...
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Momentum state normalisation [on hold]

Is the momentum state $|p>=a^{\dagger}|0>$ normalized? If yes then how do we show that? I tried using the ladder operator commutation relations but it does not give me 1.
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Quantum tunneling into a black hole

The currently accepted answer to Throwing a micro black hole into the sun: does it collapse into a black hole or does it result in a supernova? states that a small black hole of mass approximately $10^...
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Simple question on Angular Momentum

Need to know why $L^2$ and ONLY ONE of $L_x$, $L_y$, $L_z$ are constants of motion. Main problem arrives when $V = f(r, \theta, \phi)$ causing none of the $L_x$, $L_y$, $L_z$ to commute with ...
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Splitting of energy levels in solids [duplicate]

when atoms are well seperated energy spectrum is discrete, but when they come together energy levels split and they form bands, upto this i can understand. where im confused is that these splitting ...
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Is the quantum harmonic oscillator energy $E = n\hbar\omega$ or $E = (n + 1/2)\hbar\omega$? (Feynman Lectures)

Please, read the whole question. I've discussed a few contradictions and so far have not found an explanation for them. I was reading The Feynman Lectures on Physics (vol. 1), the part where he talks ...
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What if quantum mechanics and general relativity are not connected? [duplicate]

The main objective in modern physics research is to find a way to unify quantum mechanics and general relativity thorugh a series of theoretical approaches called "quantum gravity theories" But what ...
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Coherent state of second quantized hamiltonian

In my preparation for the exam I tried to solve the exercise 2.4 in Coleman's Introduction to Many-Body Physics. I like diagonalizing Hamiltonian, so I picked this problem. Also to learn more about ...
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Aharonov-Casher effect vs Spin-Orbit coupling

The Aharonov-Casher phase is the electromagnetic dual of the Aharonov-Bohm phase. It arises when a neutral particle with a magnetic moment encircles, for example, a line charge, or moves on a closed ...
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Does QM preclude well-defined conformal structure on spacetime?

My question is whether GR and QM are incompatible in a specific and severe way. GR relates the local curvature of spacetime to the local presence of matter, but QM entails that there may be no answer ...