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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37 views

How does the wavefunction of an electron “decollapse”?

In quantum theory, when an electron is sent through a slit (or multiple slits),the electron is described using probability amplitudes and is said to be in a superposition of multiple quantum states. ...
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Does a quantum channel being time-translation invariant imply that its Kraus operators commute with the Hamiltonian?

Let $\mathcal E\in\mathrm{T}(\mathcal X,\mathcal Y)$ be a quantum channel (i.e. a completely positive, trace-preserving linear map sending states in $\mathrm{Lin}(\mathcal X,\mathcal X)$ into states ...
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8 views

What are the properties and codomain of the spin $\alpha$, $\beta$?

I am following Mike Finnis on interatomic forces in condensed matter. I believe he uses the letter $s_i$ to denote spin number $\pm 1/2$ for fermions for example. But he has two functions $\alpha,\...
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What happens when the depth of the slit varies in the double slit experiment?

What meaningful effect is there if the depth of the slit varies in respect to the wavelength? Cases: D < λ D = λ D > λ
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43 views

Physical significance of the ket vector

I'm trying to understand/form an intuition for why a ket-vector, and its associated bra-vector, are appropriate tools to represent the spin of a qubit. Generally speaking, if a system has a state/...
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37 views

Susskind exercise on quantum mechanics

On Susskind book, exercise 3.1 say to prove the following: "If a vector space is $N$-dimensional, an orthonormal basis of $N$ vectors can be constructed from the eigenvectors of a Hermitian ...
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1answer
37 views

Relation between magnetic quantum number and angular momentum quantum number

The energy levels of a quantum rigid rotator are given by $$ E_{\ell}=\frac{\hbar^{2}}{2 I} \ell(\ell+1), \quad \text { for } \ell=0,1,2,3, \dots $$ It is also stated that the degeneracy of each level ...
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1answer
36 views

What can be measured in quantum mechanics and how?

This is a question about bridging reality to theory. In learning QM theory, we learn a bunch of stuff about observables, like their operators, that two quantities can be measured at once if their ...
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1answer
40 views

What happened to the factor of $\pi$ in this question?

$\\ $ I was going through the answer to this problem, when I noticed that a factor of $\pi$ in the denominator disappeared and a factor of 4 appeared in the numerator when the author started ...
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1answer
51 views

How can you know that 2 photons are occupying the same location?

Someone told me once that a photon can be in the same exact location of another photon. Because they are bosons and have spin 1 you can have billions of photons occupy the same location. I was ...
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How to derive the nearest neighbor Rashba spin-orbit coupling term?

I know that Rashba SOC can be written in the form of $(\mathbf{s} \times \mathbf{p}) \cdot \hat{z}$, but how can I get the Rashba SOC in tight-binding model :$i \lambda_{R} \sum_{\langle i j\rangle} ...
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4answers
121 views

Are Imaginary Numbers Really “Imaginary?” [duplicate]

I find the naming convention of “Imaginary” misleading, as it does give a sense that the quantity is merely an abstract construct used to mitigate the difficulties of performing some mathematical ...
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Understanding quantum models

In quantum mechanics we have different models like the infinite and finite square well, potential barrier, etc. What I don't understand is how these are applicable to real life situations. For example,...
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Why doesn't the nucleus have “nucleus-probability cloud”?

While deriving the wave function why don't we take into the account of the probability density of the nucleus? My intuition says that the nucleus is also composed of subatomic particles so it will ...
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1answer
50 views

Could brain “entanglement” explain the double slit experiment?

I know I should abandon trying to figure out quantum experiments and simply accept the various interpretations in the physics books but please bare with me and explain why my latest idea is wrong. I ...
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23 views

What are the deciding criteria for occuring of reflection, absorption, Emission, refraction and burning? [on hold]

Why does some objects reflect, refract, absorb, emit and burn, when electromagnetic wave is thrown on them? I want to know all these things at atomic and molecular level.
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132 views

Do proteins interact through classical or quantum mechanics?

For the protein interactions that occur in our cells, do they "follow" classical mechanics or quantum mechanics when interacting? I have zero knowledge about quantum mechanics, but I was wondering ...
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29 views

Quantum spin experiment and memory of apparatus

I recently started reading "Quantum Mechanics" by Leonard Susskind, and need some clarification reg. an experiment that was described in the first chapter. I'm not really sure if this is a thought ...
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2answers
97 views

What is The Heisenberg Uncertainty Principle Making Statements About?

Non-physicist here, trying to understand details about Heisenberg's uncertainty principle: Watching the The more general uncertainty principle, beyond quantum about the uncertainty principle I came ...
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56 views

Many Worlds: under which conditions does the branching happen?

I am approaching Many Worlds interpretation and I have a big question that I would like to ask you: I buy the critic moved by Many Worlds supperters to Copenhagen interpretation, saying that Bohm ...
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1answer
78 views

Why a quantum computer simulation is not a quantum computer?

Is it because the inability to generate true random numbers (I dont think so) in the host machine or something else? My understanding is that the ability to emulate a quantum computer in a ...
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30 views

Proof of quantization of angular momentum [on hold]

I have learnt that the quantization of angular momentum comes from Plank's law. Could you prove it?
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34 views

dipolar interaction [on hold]

in a magnetic material the energy of the exchange interaction between neighboring atoms is about 1 ev/atom, whereas the magnetic dipolar interaction between neighboring assemblies of atoms has an ...
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20 views

How can I prove Clebesh-Gordan coefficients are real?

I know it is convention to taken Clebesh-Gordan $<j_1,j_2;m_1,m_2|j_1,j_2;j,m>$coefficients are real.If I want to make proof it's reality from any physical defination in backward then how can I ...
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2answers
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How to interpret the wave function for non point-like objects

The accepted interpretation of a single-particle wave function is that it represents (among other things) the probability of finding the particle at any point. The wave function is normalised so that ...
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36 views

What are the best resources to master Quantum Entanglement?

I am reading Modern Quantum Mechanics by Sakurai for my semester. I read about the Quantum Entanglement, Bell Inequality and Hidden Variables theory, EPR Paradox etc. and got fascinated. I just wanna ...
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Confusion on Quantum Harmonic Oscillator Eigenvalues

In standard PDE theory, one generates eigenvalues to Sturm-Liouville problems over a finite domain. So, for a wave equation, we have an infinite number of eigenvalues $\lambda_n$ for a Dirichlet ...
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Wavefunction description [on hold]

Describe how a wavefunction summarizes the dynamical properties of a system and how those properties may be predicted. Somewhat open ended but I am having trouble contextualizing and summarizing what ...
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17 views

Time-reversal and its effect in the eigenfunctions of the Floquet operator

When time-reversal is present in a kicked Hamiltonian system (e.g. kicked rotator) it can be shown that there exists a basis in which the associated Floquet operator $U$ is symmetric. One can then try ...
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How can the annihilation of an electron and a positron create a quark-antiquark pair or a muon-anti muon pair?

The overview of this interaction is that a positron and an electron annihilate with each other and create two gamma photons which contains too much energy and soon materialise into a quark-anti quark ...
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Constructing many-body densities from Kohn-Sham orbitals

In many electronic structure methods, one solves "effective" one-particle Schrödinger equations for one-particle wavefunctions. In my case, I have Kohn-Sham orbitals from a DFT calculation. The ...
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33 views

Why can time-translation invariant quantum operations never increase coherence between energy eigenspaces?

Set $\hbar =1$. Let $U(t) = e^{-itH}$ be evolution under a Hamiltonian $H$ (for convenience let's assume $H$ is not degenerate). A time-translation invariant quantum operation $\mathcal{E}$ is one ...
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59 views

SO(3) and SU(2) [on hold]

If we define $$X(\textbf{a} )=e^{(ia_iL_i)} ,$$ how can we show that $X(\textbf{α} )$ can be written as a $2×2$ matrix in terms of 2 complex parameters $a$ and $b$ with $|a|^2 + |b|^2 = 1$, and ...
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24 views

Eigenstates in a 2D metal disk with finite-size perpendicular magnetic field (Piece-wise Gauge)

Let's have a two-dimensional metal disk with radius R, and now I apply a uniform magnetic field B perpendicular to the disk, within the concentric part of the disk with radius r $\lt$ R. How can we ...
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35 views

Spin other than integer and half-integer

I was looking at the Quantum Atlas entry for Spin which had a standard explanation Like many things in the quantum world, spin is quantized, which means that the spin of a particle is limited to ...
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14 views

Dipole moment in a bulk crystal

When calculating the dipole moment in a crystal, there is always one term neglected. This neglection is never discussed and I do not understand it at all. Assuming the Bloch functions $\Psi_{n,\vec{k}...
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3answers
75 views

How does an electron in the same shell of an atom have same energy despite of having different magnitudes of orbital angular momentum?

For example, consider the $n=2$ shell. This will have $l=0,1$ values, so correspondingly there are 2 angular momentum states having magnitude $0$ and $\sqrt{2}\frac{h}{2\pi}$. So how do these 2 ...
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1answer
33 views

Can circularly polarised light be observed deterministically in a fixed direction?

In classical electromagnetism, a circularly polarised electromagnetic wave is described by an electric field $\mathbf E(\mathbf r, t)=\mathbf E_0 e^{i(\mathbf k\cdot\mathbf x-\omega t)}$, where $\...
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64 views

What apparatus do physicists use to hold a photon and for how long? [duplicate]

While reading about one of the Chinese experiments I see that they propose to hold one half of a pair of entangled photons(meaning holding one photon for an amount of time) until they manage to send ...
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1answer
61 views

Schrodinger equation vs Feynman diagrams

If one wants to assess how an electron orbits in a hydrogen atom one uses the Schrodinger equation. Ditto for an electron in a magnetic well. However if one wants to assess how particles interact or ...
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42 views

Why do quantum computation models based on open quantum systems receive so little attention?

In almost all research on (universal) quantum computation the common models assumed from the outset are either the quantum circuit model with unitary gates, the measurement-based one-way model or the ...
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17 views

Are there stationary state solutions for semi-infinite, quantum harmonic oscillator potentials?

Suppose a quantum system obeying Schrodinger's Equation has the following potential: $$ V(x)=\frac{1}{2}m\omega^2x^2 \ \ \ \ \ \ \text{for} \ \ x\ge-a \\ V(x)=\infty \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \...
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22 views

Using FFT to find time-dependence of quantum mechanical free particle?

I am trying to visualize the time dependence of a free particle given an initial wave-function using Python and I just wanted to know if I could use the in built FFT implementation from NumPy to find ...
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23 views

Hermitian phase operator and quantum harmonic oscillator

I need to apply a hermitian phase operator $\dfrac{1}{\sqrt{1+\hat{a}^\dagger\hat{a}}}\hat{a}$ to the nth harmonic oscillator state, but I have no idea how to interpret the square root of a ...
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42 views

Are all bound states entangled?

In QM, a bound state is a special state of a particle subject to ta potential such that the particle tends to remain localized in space. The potential may be external or it may be the result ...
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16 views

Overlap of nth QHO state and momentum-shifted QHO ground state

$\newcommand{\ket}[1]{|#1\rangle}$ $\newcommand{\bra}[1]{\langle#1|}$ I have a momentum-shifting operator $e^{i\Delta p x/\hbar}$ acting on the ground state $\ket{0}$ of the QHO, and I want to compute ...
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65 views

Do “delayed choice” experiments send information back in time?

Consider the wave function collapse of a pair of entangled photons: wave function is collapsed, let's call this state '0' normal wave function, let's call this state '1' In a "delayed choice" ...
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4answers
85 views

The particle in a box problem

I'm studying undergrad level chemistry with no strong background in physics. So the problem is a little confusing to me. A few questions for clarification: Using the electron on a 2-dimensional box ...
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63 views

How a quantum particle see the world?

In a double-slit experiment, we model the electron as a wavefunction that evolves according to the Schrodinger equation. If we switch to the electron as the observer, how the experiment is described ...
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How long does photon entanglement last?

After creating entangled photons, how long does the entanglement last?