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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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What does it mean to Fourier transform a ladder operator (in the input-output formalism)?

I am currently trying to get my head around the input-output formalism. In describing the input-output formalism (link) , Gardiner and Collett take ladder operators in the Heisenberg picture and ...
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The power of quantum computer in computational physics [on hold]

With the advent of quantum computers a new era of physics computation will arrive. My question in this subject is , will quantum computers be so powerful, that we will be able to solve, the ...
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1answer
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How can we derive the formula of schrodinger wave equation independent of time? [on hold]

How did Schrodinger derive the below formula?what were the basic concept he used to derive it? $$ \frac{\partial^2\Psi}{\partial x^2}+\frac{\partial^2\Psi}{\partial y^2}+\frac{\partial^2\Psi}{\...
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1answer
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Perturbation Theory - Writing the perturbed Hamiltonian as the sum of unperturbed and the perturbation

In the time dependent perturbation theory of quantum mechanics, we start off with the assumption that the Hamiltonian of the perturbed system can be written as the sum of the Hamiltonian of the ...
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Is this how superposition works? [closed]

I know everywhere contain fields and one field can interact with another field producing interaction which is excitation of some fields so I think when there is a particle it is an excitation of many ...
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What happens when $|+\rangle$ state is sent through the control part of CNOT quantum gate?

CNOT quantum gate, with control on top path, Xgate on bottom path. If a $|+\rangle$ ket is sent to the top control part, then what happens? Does the X gate act on the bottom path ket half the time, ...
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43 views

Square root of Dirac delta Function? [duplicate]

I've puzzled by the appeareance and manipulation of a Square root of a Dirac Delta function. The article is https://www.researchgate.net/publication/...
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1answer
50 views

Representing a reducible Cartesian tensor as a spherical tensor

I'm quite confused by this transformation, and am trying to gain fluency in moving back and forth between these objects. I understand that a second order dyadic Cartesian tensor can be represented as ...
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2answers
89 views

How does a Hamiltonian 'generate' a unitary?

I know that the unitary (propagator) is given by $$U=e^{iHt}\tag{1}.$$ But I actually never saw how a Hamiltonian translates into a unitary. For example when I consider a two-level rotation in a ...
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What is the nature of vibrational relaxation in fluorescence?

As we know, electrons in fluorescent substances get excited, reaching a certain energy sublevel, only to go down through some "vibrational relaxation" to the lowest exited state possible and ...
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27 views

Confused about using uncertainty principle to determining momentum

A question asks to estimate the energy of a neutron, if the neutron is composed of a proton and electron by using the uncertainty principle. The basic idea is to let x = 1 fm and calculate p using: $...
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476 views

Is many-worlds interpretation only a philosophical matter?

Is many-worlds interpretation only a philosophical matter? It seems to me that we can't exclude a possible test for this hypothesis. I explain. For superposition principle each world would follow the ...
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1answer
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Parity of Harmonic oscillator in 2 and 3 dimensions: the case of $l_z$

From doing exercises and trying to understand their solutions, i figured in two dimensions, not all values of $l_z$ can be taken by the particles (this is to conserve parity). For example, for n=0, ...
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59 views

Trying to understand the data from “experimental delayed choice entanglement swapping” [on hold]

Sorry for the bad english! I'm trying to understand the paper "experimental delayed choice entanglement swapping", avaliable at: https://arxiv.org/abs/1203.4834 (TL:DR - they create 2 entangled ...
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1answer
36 views

How to find wavepacket time dependence from the $k$-wavefunction?

I am trying to code the time dependence of a gaussian wavepacket using the Fourier transform techniques. I began with constructing a wavepacket (real parts only at the moment) at $t=0$ by multiplying ...
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1answer
29 views

Is the disposition of $1$s and $0$s when writing orthogonal ket vectors purely conventional?

If I want to define the basis in the form of $4$-vectors, how do I proceed to make sure they are orthonormal with one $1$ and three $0$ in each vector? Is it just by convention? Does it matter if I ...
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Does something prevent superposition at our scale?

I often encounter the argument that quantum mechanics reduces to classical mechanics at sufficiently big scales, as soon as h becomes sufficiently small respect to the actions involved. I clearly ...
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1answer
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Radial term in the spin-orbit coupling

The spin-orbit interaction for the hydrogen atom is of the form $\hat{H_1} = A\frac{1}{r^3}\pmb{\hat{L}}\cdot \pmb{\hat{S}}$ Now in my course, we treated this interaction by working in the basis of ...
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2answers
58 views

Computation of $e^{i \hbar \omega a^{\dagger} a} a e^{-i \hbar \omega a^{\dagger} a}$

I need to compute terms like : $$e^{i \omega t a^{\dagger} a} a e^{-i \omega t a^{\dagger} a}$$ Where $[a,a^{\dagger}]=1$ (they are the bosonic annihilation/creation operators). I wonder if there ...
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1answer
39 views

Hamiltonian of a quantum heat bath

I have seen the Hamiltonian for a heat bath written as: $$ H_B = \hbar \int_0^\infty \omega b(\omega)^\dagger b(\omega) d\omega $$ I was hoping to understand this equation better. This suggests that ...
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2answers
65 views

Are superposition and uncertainty principles logically dependent?

If we assume superposition and define an Hilbert space with canonical commutation relations we can derive uncertainty relations. So it seems the uncertainty principle isn't required, or should be ...
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22 views

What is the 4x4 matrix for the charge inversion operator and how do you construct it?

I have a 4x4 Hamiltonian describing a part of my system. To get a holistic view of the situation I need to do a charge inversion on the matrix. What is the 4x4 charge inversion operator? And what is ...
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2answers
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What happens to the uncertainty principle when I have a particle contained within an inelastic box?

Say I have a box made of inelastic material such that when a particle hits the box, energy is lost through heat. I then put a particle inside of this box and squeeze the box down. How does this not ...
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21 views

Momentum Perturbation SHO [closed]

H=H0+H' where H' is λP^2. I need to find the first/second energy shifts of the nth energy level of harmonic oscillator (which is fine with ladder operators) Part b- Now consider the full Hamiltonian ...
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25 views

Are the Renyi entropies decreasing in the family parameter? [on hold]

Are the Renyi entropies: $$S_\alpha=\frac{1}{1-\alpha}\log(\text{tr}[\rho^\alpha])$$ decreasing in alpha? Can I have a formal proof of this?
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1answer
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What is the relationship between photocurrent vs frequency?

I'm very confused, as there are conflicting sources: Why doesn't photoelectric current increase with frequency of the incident wave? This states that frequency does not affect current because it ...
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1answer
141 views

Why don't physicists interpret randomness in quantum mechanics as ignorance or limitations in our knowledge?

As the title says: why don't physicists interpret randomness in quantum mechanics as ignorance or limitations in our knowledge? Why is the randomness in quantum mechanics equations not added to the ...
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1answer
19 views

Basis Functions for Hartree Fock, and Configuration Interaction

I'm about halfway through the book Szabo and Ostlund, and while I think I understand the rough idea of Hartree-Fock and configuration interaction, there is something I would like to clarify. For one, ...
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23 views

1D Potential Barrier Boundary Conditions (tunneling)

I'm trying to solve the boundary conditions of a 1D potential barrier for a free particle. The boundary conditions on the continuity of the wave function and its first derivatives leads to four ...
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1answer
38 views

Generator of 3D rotations in $\mathbb{C}^2 \otimes \mathbb{C}^2$

Let us consider a system of two spinors. The 3D rotation operator around the $\vec{n}$ axis in $\mathbb{C}^2$ is clearly $R(\theta) = \exp(i \frac{\theta}{2}\vec{n}\cdot\vec{\sigma})$. If I wish to ...
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1answer
48 views

Potential must be real for Hamiltonian to be Hermitian?

I have seen a few proofs specify for finite wells, step functions, and harmonic oscillators, that $V$ must be real for $H$ to be Hermitian. Why is that? If we're solving the Schrodinger equation, we ...
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Relation between spin degrees of freedom and the dimensions of Hilbert space

I came across a question which reads "Suppose the spin degree of freedom of two particles (nonzero rest mass and nonzero spin) is described completely by a Hilbert space of dimension twenty one. ...
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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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1answer
102 views

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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1answer
80 views

Solution of the coupled non-linear oscillators by using perturbation theory [on hold]

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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1answer
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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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1answer
103 views
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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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2answers
87 views

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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1answer
63 views

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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2answers
47 views

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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3answers
138 views

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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3answers
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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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0answers
27 views

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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2answers
107 views

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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1answer
87 views

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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30 views

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 ...