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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48 views

Scattering states for even potential in 1D

E.g. For a finite square well that has the following potential: $$ V(x)= \begin{cases} 0, & |x|>a \\ -V_0, &|x|\leq a ...
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Why we are not using Lagrangian instead of Hamiltonian in non-relativistic quantum mechanics? [duplicate]

Why we are not using Lagrangian instead of Hamiltonian in non-relativistic quantum mechanics?
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1answer
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How to find the constants $a$ and $b$?

We consider the motion of a particle without spin submitted by the hamiltonian $H$ defined by the eigen-value equation:$H|n_1,n_2\rangle =(n_1^2+n_2^2)|n_1,n_2\rangle $ the proper kets of $H$ verify ...
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121 views

What is meant by “spontaneous creation” in this paper?

https://arxiv.org/abs/1404.1207 I have some questions in regard to this paper. If I am not mistaken it is akin to Alexander Vilenkin's proposed cosmological model that has the Universe begin to exist ...
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12 views

General structure of parity preserving two qubit gate

I am trying to decompose a set of two qubit gates repecting parity, though I am not sure whether parity is the right word for this. The gate has the following structure: $$\begin{bmatrix} u_{11}&...
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35 views

Why coefficient of states for non-positive Hamiltonian matrix are all non-negative?

For a Hamiltonian $H$, if the all elements of matrix is non-positive under a set of basis $\{|\phi\rangle\}$:$$\langle\phi|H|\phi'\rangle\leq0$$ then the ground state of $H$ will be the linear ...
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11 views

Symmetry of the scattering super-operator

Suppose we have an initial ensemble described by a density matrix $\rho$ and any given member of the ensemble scatters from one of some set of scattering matrices $\{S_g \equiv O_g S O_g^\dagger : g \...
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101 views

In quantum mechanics, which concept caters for light rays?

If photon wavefunctions are omnidirectional and don't have a definite size, how comes those from the Sun don't all collapse on Mercury and some do actually reach Earth ? I understand that ...
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9 views

Writing a particular state (spectroscopic notation) as a superposition of n,l,s,ml,ms states

For a hydrogen atom in a particular state, e.g. $|3^2d_{\frac{3}{2}}(m_j=\frac{-1}{2})\rangle$, how would I decompose this as a superposition of $|n,l,s,m_l,m_s\rangle$ states? For example, I ...
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1answer
322 views

How to think of matrices as observables?

I'm reading Nielsen and Chuang. In one of the early chapters, they introduce some matrices such as $$X = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}.$$ They interperet this as a gate that ...
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2answers
121 views

Born: matter particle not to be interpreted as wave packet?

In his excellent book "Atomic Physics", after showing that the velocity of a group of waves equals a particle's velocity, Max Born writes that to interpret a particle of matter as a wave packet due ...
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94 views

How do you experimentally distinguish $\psi_1 \otimes \psi_2$ and $\psi_2 \otimes \psi_1$?

What I am asking is that $\psi_1 \otimes \psi_2$ and $\psi_2 \otimes \psi_1$ are obviously different states. However, theoretically a measurement can be done that these to states will give two ...
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23 views

Interference in “Frustrated Two photon Creation”

In this paper it is explained how an SPDC source can have its emission inhibited by destructive interference with emission from a previous time. I have had a (maybe incorrect?) general intuition ...
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38 views

Dirac equation boundary conditions

In Schroedinger equation, which is second order differential equation, one normally, equates both $\psi(x)$ and $\psi'(x)$ across the boundary, as boundary conditions. However, the dirac equation ...
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29 views

Can someone help in applying covariance condition to this unitary transformation?

I am trying to apply covariance property on this Quantum adder transformation in which a two particle input state is mapped onto a two particle output state. I am trying to represent these states into ...
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2answers
78 views

Physically intuitive explanation for Hamiltonian of charged particle in EM field

I've recently been looking at the quantum mechanical description of a charged particle in an EM field and have come across this classical Hamiltonian: $$H = \cfrac{(\mathbf p - q\mathbf A)^2}{2m} + q\...
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Three dimensional visualization of a qutrit

My question is in reference to the paper "Three dimensional visualization of a qutrit"(https://arxiv.org/abs/1601.07361). The author's start with a symmetric two qubit density matrix written in the ...
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Does Quantum Eraser erases results from past ( like we can prove by carbon dating etc )? [on hold]

is it proven by Carbon - dating or something similar to prove age? [ by this I want to understand that particles actually see future ] Is there any proof that does it with techniques "like" carbon-...
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1answer
75 views
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Ohmic spectral density

I am witting a paper about the non-Markovian effects of open quantum systems (a qubit interacting with a bosonic environment). I am using a spectral density of the form below: $$ J(\omega) = \frac{\...
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2answers
112 views

Solution of Schrodinger equation

I am reading 'Particle in 1 dimensional box' and 'Potential step' in Quantum Mechanics. In the figure shown we have two same looking schrodinger equations, equation 1 and equation 2. Why solutions of ...
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1answer
96 views

What made Born interpret $|\psi|^2$ as a probability density?

What was Born reasoning when he introduced the rule that $|\psi|^2$ could be interpreted as a probability density?
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1answer
22 views

Quantum statistics of a particle in a magnetic field

Let us consider the statistical physics of a single particle (without spin) moving in a magnetic field described by a vector potential $\vec{A}$ at a finite temperature $1/\beta$ on a $2$-dimensional ...
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Proof of Ohm's Law [duplicate]

I was watching MIT OCW 802 and the lecturer mentioned that Ohm's law has a proof by quantum mechanics. The video is here- https://m.youtube.com/watch?v=PJqOaHBgr30 And the lecturer makes the claim ...
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Does shining a neutron beam with Xrays/photons of pair production potential > 1.022MeV accelerate neutron decay? [on hold]

Confirmed experimental data is the looked after answer. Pure, simple , straight forward. edit: beamed or bottled/cold neutrons, either works.
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How is conditional probability handled in quantum mechanics?

In ordinary probability theory the conditional probability/likelihood is defined in terms of the joint and marginal likelihoods. Specifically, if the joint probability of two variables is $\mathcal{L}(...
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Is quantum which-way information the real cause? [on hold]

I say all that matters is state. Which-way has nothing to do with it. State change is something that happens to a particle while in flight. The final panel is wave collapse and doesn't effect the ...
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2answers
35 views

How does Cosmic microwave background radiation provide temperature to the outer space?

We define temperature as average kinetic energy of atoms. We know that outer space has vacuum that is it lacks matter and hence the temperature should be 0 K. But because of CMB radiation, the ...
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3answers
72 views

What was the energy of light thought to be before Einstein

I'm studying the photoelectric effect where it turned out that the kinetic energy of the emitted electron was dependent on the frequency of the u.v. light and not its intensity. It was previously ...
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1answer
43 views

Do quantum effects of macroscopic objects dissapear because of decoherence or because large objects have small wavelenghts, or both?

I’ve read that the wavelength of macroscopic objects is so small that it’s effects are negligible so the object can be described with classical physics, and that decoherence causes quantum effects to ...
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3answers
89 views

Does a photon's wavelength (and energy) change when reflecting off a mirror?

The momentum of a photon is $\ p=E/c.$ When a photon reflects off a mirror, it is elastic scattering. Elastic scattering should keep the energy of the photon. But radiation pressure states, that ...
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1answer
125 views

Spin precession for Rabi oscillations : interpretation with magnetic field in rotating frame

The model considered Consider an atom modeled by a two level system of energy $\hbar \omega$. We assume this atom is interacting with an electric field through electric-dipole interaction. The full ...
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37 views

Double-slit experiment with erasing all the collected data

The question concerns the double-slit experiment with collecting the data to register through which of the slits every single photon has passed. As I understand, in this case, when the photons are ...
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1answer
29 views

Quantum probability distributions via canonical traces

Given $N$ distinguishable quantum particles in the canonical ensemble, we can estimate the probability of finding one of those, labelled by $j$, in a certain position $x\in\mathbb R$ by computing \...
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1answer
231 views

Quantum master equation and off diagonal terms

I have a couple of related questions What is exactly the difference between the quantum master equation and the regular master equation? My understanding is that the normal master equation is used to ...
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1answer
48 views

In quantum mechanics, is energy conservative statistically or for every single system? [duplicate]

I'm learning from Griffiths' book "Quantum Mechanics". In quantum mechanics, a particle has a variety of accessible energy states. Then is the energy of the particle always conserved? Energy states ...
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1answer
657 views

Conservation of energy and wavefunctions

I'd appreciate a bit of clarification on how conservation of energy works in QM. The infinite square well has a set of stationary states, each corresponding to one of the discrete energy levels of ...
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18 views

Why is the spin-orbit interaction for a nucleus so much more important than the spin-orbit interaction in atomic physics?

In atomic physics, the spin-orbit is a small correction between 1/1000 and 10ppm, so fairly small. In contrast, in nuclear physics the inclusion of the spin-orbit interaction is necessary to reproduce ...
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4answers
10k views

Does the mass of an electron change with its “energy state”?

When an electron absorbs a photon, it gets into a higher energy state and goes into the upper orbit/shell. Does (rather should) this absorption of energy also have an impact on its mass (although ...
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3answers
585 views

Is zero-point energy real?

In the context of canonical quantization, the ground state/zero-point energy of a harmonic oscillator is $$ E_0 = \frac{1}{2}\hbar \omega. $$ The vacuum is alleged to be permeated with this zero-point ...
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1answer
134 views

Domain space of compatible and incompatible operators (observables)

Sakurai (Modern Quantum Mechanics, by J.J. Sakurai) states in the section on compatible operators: Let us first consider the case of compatible observables A and B. As usual, we assume that the ket ...
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1answer
186 views

Relativistic Doppler effect and Quantum Mechanics

Consider the situation below. I’m at a point in space along with a bunch of detector away from any gravitational field. I see a star moving away from me at a relative speed of $$v$$by measuring the ...
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3answers
113 views

Von Neumann entropy in terms of the mutual overlap?

I have $N$ pure, but nonorthogonal, states $|\psi_n\rangle$ with density matrix $\rho_n=|\psi_n\rangle\langle\psi_n|$. Say we call the the total density matrix $\rho=\frac{1}{N}\sum_n \rho_n$. Are ...
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34 views

Energy or a piecewise defined wave function in an Infinite Square well

So I'm asked to determine the most probable measured energy value of a particle in an infinite square well with wave function $$\psi(x)=\begin{cases} Ax, & 0< x<\frac{a}{4} \\[1em] ...
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60 views

Limit of the $\sin^2$ function in the derivation of Fermi's golden rule

In the derivation of Fermi's golden rule one typically arrives at an expression of the form $$ \frac{\sin^2(\omega t)}{\omega^2} $$ which is then converted to $$ \pi t\delta(\omega). $$ I cannot ...
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31 views

Why do quarks flip chirality when exchanging an instanton?

Quarks are elementary particles, part of the SM. There are a lot of different questions and answers on this site about chirality, I did not find a really good description, so I will use this wiki ...
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35 views

Can we calculate and identify all allowable EM packet frequencies? [on hold]

Photons come in discrete packets, yes? Wavelength/frequency measures packet energy, yes? Not all frequencies can exist, or we would have a continuous spectrum and infinite energy, yes? Planck's ...
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1answer
197 views

First-Order Perturbation of Energy Eigenfunction

I have a homework questions where I'm struggling to understand the methodology to use. We derive first the energy functional for the energy eigenfunction equation (this is fine, I used some vector ...
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2answers
89 views

The overlap of two Gaussian states

According to e.g. Serafini (Quantum Continuous Variables), the Hilbert-Schmidt product ('overlap') of two multimode Gaussian states $\rho_1,\rho_2$ is $$\text{Tr}[\rho_1\rho_2]=|\langle\psi_1|\psi_2\...
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1answer
116 views

Intuitive understanding of the derivation of the Rayleigh-Jeans law

I know the Rayleigh-Jeans law and how the formula predicts UV catastrophe. Without getting into the exact derivation, I am trying to get some intuitive understanding of it by using some of the broad ...
2
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1answer
139 views

Understanding the Plasmon dispersion relation to first approximation

Plasmons are quantized oscillations of the charge density in solids, and are found in basically all conducting materials in nature. As I am playing around with an electron microscope I refurbished, I ...