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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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How to find a CSCO of an eigenfunction?

So, say you have an eigenfunction defined as: $\psi \left(x_1,x_2\right)=\int _{-\infty }^{+\infty }\:e^{p\left(\frac{2\pi i}{h}\right)\left(x_1-x_2+x_o\right)}dp$ (The spinless 2 particle system ...
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Applying Sylvester's theorem in quantum mechanics

A $2d$ system consists of $N$ identical cells arranged linearly in series. The transfer matrix of a single cell is an unitary Hermitian $2$x$2$ matrix with eigenvalues $\exp(±i\theta)$. I need to use ...
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Proposed experimental cosiderations of a micro-mechanical oscilator in a superposition state

This question asks about the experimental result that is theoretically expected or is know already from experience, when one considers the following two scenarios for the micro-mechanical oscillator ...
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Is causality a universal law?

Sorry, I'm not very confident on my understanding of anything at a quantum level and superpositions have me wondering....
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Delayed choice quantum eraser without randomization?

My understanding of delayed choice quantum eraser experiments roughly corresponds to the Wikipedia article about them, so please forgive if this question is stupid. In all delayed choice experiments ...
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28 views

Operators evolution

I have a little question about equation for creation/annihilation operators. Usually we obtain time evolution equation for these operators from Heisenberg equation. for example: $$\frac{da_l}{dt} = -...
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Could an electron enter the nucleus, and if so would it be captured by a proton?

I've been trying to find an answer to this question, but have come across contradictory answers, and have limited knowledge of quantum mechanics myself. Almost all the threads (here and on Quora) ...
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Is it possible to see revivals using lowest order time evolution in Jaynes-Cummings

I'm trying to implement Monte Carlo Wave Function method in the standard Jaynes-Cummings model $$ H_{JC} = \frac{\Delta}{2}\sigma_z + a^\dagger a + g(\sigma_+ \otimes a + \sigma_- \otimes a^\dagger)....
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Electron diffraction on crystal lattice

To observe electron diffraction, we standardly let its wavefunction pass trough a crystal lattice. However, why does not the electron's interaction with crystalline atoms cause wavefunction collapse?
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Exchange stiffness for HCP

I am studying the exchange interaction, which can be described with the Heisenberg Hamiltonian: $\hat{H} = -\sum_{i,j}J_{ij}\hat{\mathbf{S_i}}\cdot \hat{\mathbf{S_j}}$ In the framework of constant ...
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15 views

What is the flux $\Phi$ enclosed by cyclotron orbit, which can express the quantization rule?

Suppose an electron (mass $m$, charge $e$) in the xy-plane with $B=(0,0,B)$ (The classical EOM result in circular orbit). Using the Bohr-Sommerfeld quantization rule we can find that $E_n = (n+1/2)\...
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Conjugate of total spin operator

I got a lattice, and the total spin operator for x and for y, for that lattice. I know that the x component conmutes with an operator called staggered spin operator in y. I also know that the ...
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Ground state of two fermions coupled with one boson

I have an Hamiltonian of the form: \begin{align} \begin{aligned} H _ { 1 } & = f _ { 1 } \otimes b ^ { \dagger } + f _ { 1 } ^ { \dagger } \otimes b \\ H _ { 2 } & = f _ { 2 } \otimes b ^ { \...
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How do we observe an electron? [duplicate]

When an electron is observed it acts like a particle and its wave function collapse. This statement is very famous in quantum mechanics, but what is meant by observing an electron? Which devices are ...
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Spin-orbit interaction for titanium in the excited state $(3d)^1(4p)^1$

Let's look at a Ti-atom in an excited state with 2 valence electrons $(3d)^1(4p)^1$. What term schemes $^{2S+1}L_J$ do we have for this state considering spin-orbit interaction? My take: For both ...
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A unitary that induces Entanglement Breaking Channel for any ancillary state

Let's say there is a unitary operator $M:\mathcal{H}_1\otimes\mathcal{H}_2\to\mathcal{H}_A\otimes\mathcal{H}_B$ such that the channel $\Phi$ given as $$\Phi(\rho)=\text{Tr}_BM(\rho\otimes\phi)M^\...
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1answer
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Quantum tunneling in a capacitor

Ampere's law of Maxwell's equation includes displacement current as the Maxwell's correction. Suppose consider a capacitor with a thin distance of separation. For an applied voltage do they posses ...
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37 views

Compactness and Quantization

So I was thinking today about when observables become "quantized", and came to the conclusion that every instance of quantization I've ever come across has come about from solving the Schrödinger ...
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1answer
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How do we know what happened during the Planck epoch era of the big bang?

The Cosmic Microwave Background provides the left over radiation of the big bang. Cosmologists have theorised what happened at the Planck epoch era of the big bang. Where is the evidence of what ...
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What is the meaning of “representation of the canonical commutation relation in the form of Heisenberg for symplectic locally convex space”?

What is the meaning of "representation of the canonical commutation relation in the form of Heisenberg for symplectic locally convex space"?
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1answer
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Why does Fluorine-19 have a nuclear spin of 1/2?

According to the nuclear shell model, $^{19}F$ has one unpaired proton in the $6$-fold degenerate $1d_{5/2}$ state, which means the orbital angular momentum is $l = 2$ and the total angular momentum ...
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How is quantum mechanics consistent with statistical mechanics?

Let's say we have an harmonic oscillator (at Temperature $T$) in a superposition of state 1 and 2: $$\Psi = \frac{\phi_1+\phi_2}{\sqrt{2}}$$ where each $\phi_i$ has energy $E_i \, .$ The probability ...
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2answers
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Why did Planck took frequency from a wave and incorporated it to explain particle behavior of light?

Well if we assume anything to be a particle then it can never be a wave right?? But when planck developed his idea then he incorporated the frequency into the formula E = hv but frequency is a ...
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What happens when we cool down the gas of non-identical particles?

For gas of identical particles, when we cool it down to extremely low temperature we can see one of two types of behaviour depending on the symmetry of wavefunction with respect to argument ...
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Prove Dipole moment of an isolated quantum system in isotropic space is identically equal to zero, unless there exists an accidental degeneracy [on hold]

Dipole moment of an isolated quantum system in isotropic space is identically equal to zero, unless there exists an accidental degeneracy. How to prove this?
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3's a crowd. Particle me but may i have this dance? [on hold]

In a particle accelerator (built for 3 particles), could we smash them into a vacuum with only enough space for 2 particles?(electrons, protons, neutrons) what would be the result?
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Is $c^{\dagger}|\psi_N \rangle= \sqrt{N+1}| \psi_N \rangle $ or $c^{\dagger}|\psi_N \rangle= | \psi_{N+1} \rangle $ in case of fermions

For the $N$ fermion state, when we apply creation operator $c^{\dagger}$, should we write the factor $\sqrt{N+1}$ with the resultant state, like $c^{\dagger}|\psi_N \rangle= \sqrt{N+1}| \psi_N \rangle ...
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How can I plan my physics learning? [on hold]

i would like to start learning physics on my own, but the problem is i dont know where to start, and what topics i should do after, Im a 16 year old learning at a high school with high level phycics, ...
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Quantum Potential - how to find its eigenstates?

I am studying the Pöschl-Teller potential in spherical coordinates and doing a change of variable is enough to put it in another sort of differential equation and thus, obtain the solution. The point ...
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3answers
350 views

What are the experiments performed to determine the position of an electron inside an atom to verify the probability wave function data?

What are the experiments performed to determine the position of an electron inside the atom to verify the probability wave function data? Is it possible to do those experiments in real life?
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1answer
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Tensor product of Hilbert space and Fock space

If we have system consist of two or more than two subsystems, we can write hilbert space of a system in terms of tensor product of Hilbert spaces of subsystems and we can write state of a system. But ...
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1answer
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Can the problem of the infinite energy of an electron's point charge be solved by applying time constrains?

Just because an electron's energy and mass appear to be infinite does not necessarily mean you would measure infinite energy and mass. Since measuring the mass of something generally involves you to ...
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1answer
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Example of mixd entangled state [duplicate]

I'm looking for specific examples of all combinations of pure, mixed, separable and entangled states, but I would prefer if they all have some physical significance. For pure states, the separable ...
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1answer
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Is it possible to prepare thermal state by performing a single mode quantum operation on vacuum states?

Let me define thermal state as \begin{equation} \rho=\sum_{n=0}^{n=\infty}\frac{\bar{n}^n}{(\bar{n}+1)^{n+1}}\left|n\right>\left<n\right|. \end{equation} is it possible to prepare this state ...
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Is it possible to jump in space [on hold]

A system of nonlinear equations can have many branches of roots, for example, a system of equations of general relativity by substituting $$g_{pq}=\sum_{k=1}^N c_{pqk} \phi_k (t,x^1,x^2,x^3),c_{pqk}=...
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1answer
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Where is quantization used in deriving Planck's law?

There are several explanations for how Planck used quantization to explain blackbody radiation correctly without the ultraviolet catastrophe. I will follow this explanation. For a cavity, the mode ...
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Zero field splitting only defined for $S>\frac{1}{2}$?

Why do we only consider the spin-spin interaction between unpaired electrons? For reference the wikipedia page for zero field splitting says The classic case for ZFS is the spin triplet, i.e., the ...
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1answer
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The role of the harmonic oscillator eigenfunctions in quantum optics

In quantum optics we quantize the electromagnetic field and describe it using the harmonic oscillator model and the formalism of annihilation and creation operators. For the electric field operator we ...
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Vs = x* r what does it mean? [on hold]

A few weeks ago a friend of mine gave me this calculation but i don't know what it means. I've tried to ask it to my teacher and some friends but they also don't know, I suspect it is about quantum ...
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What is effective mean value? [on hold]

For counting the number of particles in any specific state we use effective mean value $\langle \hat{N} \rangle $ instead of number operator $\hat{N}$ in ensemble. I want to know what is the advantage ...
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What's the difference between coin flipping and quantum physics?

Watching this TED video, which explains about Quantum Physics, I'm confused, please let me ask a question. There is one coin whose state is "Head" on the table. First, the computer decides whether ...
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Calculating the evolution at any moment $t$ of a density matrix

I was reading the paper https://arxiv.org/abs/1303.4686, where we are given $N$ systems, all with the same Hamiltonian $$H=\sum_i \varepsilon_i \mid i\rangle\langle i\mid ~,$$ such that the joint ...
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1answer
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Explanation of Different factor of $2$ in Formulas for the Uncertainty Principle [duplicate]

I am readind about Heisenberg's Uncertainty Principle and although the main formula most texts use is $$\Delta x\Delta p_{x}\geq \frac{\hbar}{2}$$ or equivalently $$\Delta x\Delta p_{x}\geq \frac{h}...
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If photons have no mass, why do they gain mass in photon entanglement?

Photons are massless particles. However, this article states that photons can gain mass when they become entangled. How can this happen? From the article: Physicists create new form of light ...
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Property of time evolution operators

I am trying to show that: $\langle0|\Pi^n_{i=1}\psi(t+t_i,x_i)|0\rangle$ is independent of time. What I did is to write everything in terms of the Schrodinger picture operators which I know are time-...
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Difference between pure and thermal states

As far as I know by inserting a harmonic potential $V(x) = \frac{1}{2}m \omega x^2$ into the time-independent schrödinger equation I can obtain the wave-functions eigenstates and eigenvalues (energies)...
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Bound on Quantum Chaos

I am currently reading the paper A Bound on Chaos. In this paper, they evaluate the quantity C(t), which is an out-of-time-order correlator (OTOC), and use very clever arguments to show that there ...
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1answer
152 views

What if Schrödinger's cat's meowed?

Sorry if this has been asked (every similar question has a title that basically tags Schrödinger's cat) If after the superposition of the cat being dead and alive at one time was created, and the ...
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Is mode and orthonormal set of a particle same thing?

Let say we have a particle $A$ belongs to Hilbert space $H_A$. The complete orthonormal st of a particle is $\sum_{n=1}^{\infty}|\phi_n \rangle$ belonging to hilbert space $H_A$. Now if we write state ...
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Conceptual understanding of Harmonic oscillators in Thermal states

my professor in the lecture defined a general thermal 'state' (which actually is a density matrix) in the following way $$\tau(\beta) = \frac{e^{-\beta H}}{Z}\tag{1}$$ where Z is the partition ...