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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60 views

How to differentiate an operator in QM?

I recently started learning QFT and the lecturer wrote down some equations for a quantum harmonic oscillator: $$\hat H= \frac{\hat p^2}{2m}+\frac{1}{2}mw^2\hat x^2$$ $$\partial^2_t \hat x=-w^2\hat x$$ ...
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A small alteration to the Afshar experiment

I found a setup of Afshar experiment in Fig. 3 of this Wikipedia link. I assume that the setup shown in Fig.3 is accurate (Sorry for using Wiki as a link). https://en.wikipedia.org/wiki/...
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48 views

Theoretically, is the possibility of quantum superposition at the macro level possible?

We know that quantum overlap has currently managed to do so in up to 2000 atoms, more and more limits are breaking.
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45 views

Proof that the momentum operator is hermitian without assuming the wavefunction approaches zero at infinity?

I am currently taking my second semester of quantum mechanics. For a number of proofs in the course, we have used the assumption that the wavefunction goes to zero at infinity. We have simply used the ...
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Quantum Mechanics And Cauchy-Riemann Equations

A complex valued function in complex variable $z$ can be used to represent the potential and field lines of the electric field in 2 dimensions: Some notes on the method of Conjugate Functions This is ...
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1answer
56 views

Why is time-evolution unitary - The Heisenberg-picture Version

There are various versions of this question already on this site, which attempt to justify / make plausible that the time evolution of quantum mechanical observables is unitary. Most of these ...
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16 views

How does a phase shifter for an electron beam work?

It is well known that if we insert a phase shifter behind one of the slits in a double slit experiment, the interference pattern gets altered. In mathematical terms this follows because only one ...
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16 views

What are some good model quantum systems in external electric fields?

I want to understand a few things on the behavior of atoms and molecules in (weak, non-ionizing) external electric fields. For this, I am looking for model systems that might have an easily ...
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1answer
57 views

What does it mean to simulate a quantum system?

What does it mean by simulating quantum system? Can I simulate Young's double slit experiment with a quantum computer? If yes, won't it violate no-cloning theorem?
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Question regarding radial raising/lowering operator for isotropic harmonic oscillator

I understand the symmetry structure of the 3D isotropic harmonic oscillator $H = \frac{\mathbf{P}^2}{2\mu} + \frac{1}{2}m\omega^2\mathbf{X}^2$ as follows. The energy levels are $E_N = \hslash \omega (...
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Representation of time evolution operator and spectral decomposition

I was preparing for my quantum mechanics exam, and I came to think about this question regarding the spectral representation of time evolution operator. Let's say we are given the Hamiltonian: $\hat{...
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Why are numerical solutions for the Schrödinger equation necessary?

Suppose a particle in free space given by: $\psi(x,t) = Ae^{ik(x-\frac{\hbar k}{2m}t)} + Be^{-ik(x-\frac{\hbar k}{2m}t)}$ Why are numerical solutions necessary in order to plot this? Why can't ...
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Slater Koster Tight Binding Method

I am reading the paper (J. C. Slater and G. F. Koster, Simplified LCAO Method for the Periodic Potential Problem, Phys. Rev. 94, 1498, also here) about Slater Koster tight binding method. I can ...
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Is pair production a type of elastic scattering?

Pair production is the creation of a subatomic particle and its antiparticle from a boson. Pair production often refers specifically to a photon creating an electron–positron pair near a ...
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18 views

Differences between thermal average and ensemble average

Studying tunneling phenomena in the Interaction Picture, I stumbled upon the definition of the tunneling current as the expectation value of the current operator: \begin{equation} I = \left\langle \...
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1answer
92 views

Do Hermite polynomials imply a weight for quantum harmonic oscillator wavefunctions?

I know that solutions of quantum harmonic oscillator can be expressed in the form of Hermite polynomials. But I recently came to know that Hermite polynomials are actually orthogonal polynomials ...
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1answer
45 views

Are operator matrices of $x$ and $p$ the same for all systems?

I recently read Computing quantum eigenvalues made easy . In that article, the author used the position and momentum operator's matrix form in terms of the normalized eigenstates of a harmonic ...
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3answers
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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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2answers
70 views

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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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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1answer
29 views

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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1answer
68 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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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
43 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
42 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
42 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
65 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
130 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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3answers
36 views

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
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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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25 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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3answers
138 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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1answer
33 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
102 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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3answers
57 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
81 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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0answers
33 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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35 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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1answer
56 views

How can I prove Clebsch-Gordan coefficients are real?

I know it is convention to taken Clebsch-Gordan $\color{blue}{<j_1,j_2;m_1,m_2|j_1,j_2;j,m>}$coefficients are real.If I want to make proof it's reality from any physical defination in backward ...
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2answers
38 views

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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38 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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0answers
51 views

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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29 views

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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18 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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2answers
51 views

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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37 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 ...