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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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Proving co-rotated time derivative is objective

So I need to show that: $$ \mathring{u}^+ = Q\mathring{u} $$ My progress is thus far, since a vector is objective (i.e. $u^+=Qu$): $$ \mathring{u}^+= (\mathring{Qu}) = \dot{(Qu)}-w(Qu)=\dot{Q}u+Q\...
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Is $\langle \phi_m|\dot{\phi}_n\rangle$ assumed real in electronic excitation theory?

I'm studying a topic of the Nikitin's book (see pages 101 and 105) which deals with nonadiabatic electronic transitions, considering the two-state approximation. I think that the author make ...
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28 views

Quantization of complex Klein-Gordon field in curved spacetime

The quantization of a scalar field in curved spacetime usually goes along the following lines. The minimally coupled scalar field lagrangian is $$\mathcal{L}=\nabla_a\phi \nabla^a\phi^\ast - m^2\phi^\...
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How do you know when two objects are so called entangled?

I’m not asking how would you entangle two objects. I want to know how would you know they are entangled?
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34 views

The equivalent of vector addition for density operators?

In quantum mechanics, pure states may be represented by (subspaces spanned by) vectors in a Hilbert space, which may be added. This is physically meaningful, and in wave mechanics leads to visible ...
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31 views

Derivation of the Berry Curvature and Bloch Magentic Moment in Graphene

I am attempting to derive equations 2 and 6 from Xiao et al. paper "Valley contrasting physics in graphene" (Link to paper). The Hamiltonian for graphene with a staggered sublattice potential (in ...
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Why do we derive more fundamental quantum theories from less fundamental classical theories? [duplicate]

In almost every derivation of a quantum theory (quantum mechanics or quantum field theory), we start with a classical theory using classical equations and quantize it (by imposing certain constraints ...
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Why is this Pilot-wave model on a discrete spacetime is stochastic? [duplicate]

In Gluza & Kosek (2015) (DOI 10.1007/s10701-016-0026-7; paper available at Springer (NB: PDF)) It introduces a pilot-wave model on a discrete spacetime lattice. However, the pilot-wave model is ...
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59 views

About the von Neumann entropy after the partial trace

In the quantum information field, it is widely known that the von Neumann entropy of a state $\rho$ is 0 if and only if $\rho$ is a pure state. If we restrict the state as a pure entangled state, is ...
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43 views

Sending Information With Entangled Particles

I learned from my quantum mechanics course that if you measure a quantum state twice, two things can happen: 1) You take the second measurement just after the first on. In this case, the result will ...
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Spacetime as an independent yet interacting frame of reference for QM. Looking.for papers [duplicate]

We know that GR and QM are both valid and verified and yet for some reason they just don't want to go together. We say QM describes the microscopic while GR describes the macroscopic. I was thinking ...
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Is any given triplet spin state an eigenstate of some $j^z$ in the correct basis?

Imagine you have a triplet spin state, which in general can be written as $$|\psi \rangle = \alpha | \uparrow \uparrow \rangle + \beta ( | \downarrow \uparrow \rangle+ | \uparrow \downarrow \rangle) ...
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Is there any Feynman diagram for Baryon/Hyperon decay with missing energy?

I am reading the hyperon decays with missing energy this paper tells for the prospects of baryon decays with missing energy I want to know some of the Feynman diagrams for hyperon decays. Can anyone ...
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What qualifies as a quantum theory and why are we seeking a quantum theory of gravity? [duplicate]

When can a theory be called a quantum theory? Does it have to do with the existence of certain quantities which take discrete values (they increase in quanta)? Or does it have to do with the existence ...
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Why do we use this diagram/model for elementary particles?

The model of elementary particles is analagous to the periodic table, which is organized not only beautifully, but also functionally. The typical model for the elementary particles that pops up ...
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Domain of a Hamiltonian

In a recent paper (on an exactly solvable toy model and its dynamics), we studied such a toy model: $$ H = \sum_{n\in \mathbb{Z}} n |n \rangle \langle n | + g \sum_{n_1,n_2 \in \mathbb{Z}} |n_1 \...
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As electrons are present in many places at the same time so how can it not violate conservation of energy?

I was just wondering that as according to quantum mechanics electrons are present in many places at the same time, now as according to Einstein as $$E = mc^2$$ doesn't it violate energy ...
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Problem with an exchange integral

I'm reviewing the chapter on molecules from Gasiorowicz's Quantum Physics book (Ch. 20 of 1st edition) and it gets to a part where it solves the $H_2^+$ ion using the variational principle. There are ...
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What is the simplest model of a quantum measurement on a 2 level system

What is the simplest physical system which can be used to model the quantum measurement of a 2 level system? For example, can the following, spin coupled to a harmonic bath, be used to model a ...
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29 views

Is a dichotomic basis possible for 3-dimensional space?

We know that the Pauli basis for the 2-dimensional space is a dichotomic basis in the sense that every Pauli matrix has two distinct eigenvalues. Is it possible to express a 3-dimensional matrix $\...
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Spontanous emission Hamiltonian model

I am looking for a clear (and not too long) model of spontaneous emission, for an atom modeled by a two level system in a cavity where the field is multimode I am looking for model bases on ...
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Pauli exclusion principle for non-stable states

If an electron partially occupy $1s$ orbital, can other electron occupy $1s$ partially, too?
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62 views

How can I use the Wronskian to show the following relation? [closed]

I cannot solve the part(a) and (b) mathematically. Have no idea how to start solving the problem by using the property of wronskian.
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Is time-evolving wave function verified by direct measurement?

In quantum mechanics, if we know the initial wave function and the external potential, we can predict its wave function in any future point in time with Schrodinger's equation. Is there direct ...
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The Implication of the Gravitational Constant in the Planck Mass [duplicate]

Why is it considered acceptable to derive an expression for the Planck mass [mP] using the gravitational constant G simply because the resulting units are of 'mass' when it is far from clear what the ...
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Does observation in quantum theories always imply interaction (affecting quantum system with photons, electromagnetic fields, etc.)?

The term observation is obscure. As I see so far, observation is always done by means of affecting (!) the quantum system by some means - often photons or electromagnetic waves or whatever else. ...
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What are Bohmian trajectories for a free electron?

A free electron, or any other quantum particle, has an uncertain position/momentum, according to Heisenberg uncertainty principle. The squared amplitude of the wavefunction determines the probability ...
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1answer
56 views

Coherent state under Kerr evolution

I have a bosonic mode associated to the usual operators $a$, $a^\dagger$. I'm interested in knowing the evolution of a coherent state $\vert \alpha \rangle = e^{\alpha a^\dagger - \alpha^\ast a}\vert ...
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30 views

What is the physical meaning of the zeroness of the antidiagonal of the matrix representation of $\textbf{n}\cdot\textbf{S}$ operator?

I encountered a problem where I had to use $\textbf{n}\cdot{\textbf{S}}$. It was found to be: What does it mean physically, that the antidiagonal of this matrix is 0, for any $\textbf{n}$?
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1answer
85 views

Doubts about the use of tensor product In quantum mechanics

I'm studying quantum mechanic in particular tensor product and Hilbert space (for the first time). I have some doubts and I would like to check if I have understood correctly. Factorization The ...
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3answers
51 views

Self-interaction in spin-orbit coupling?

In spin orbit coupling, in an atom motion of electrons about nucleus generates magnetic field and we consider this field to interact with magnetic moment of electron. It sound strange as in ...
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1answer
80 views

Is this a correct argument why $c$ is the cosmic speed limit, and what does it mean for the speed of massless particles? [closed]

I am now in my second bachelor, taking both an electrodynamics and a quantum mechanics course. This made me think of an argument to explain why particles cannot exceed the speed of light. So far I ...
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Can the reduced state of a mixed entangled state be pure?

For an entangled pure state, the Schmidt decomposition is such that there are at least two non-zero Schmidt coefficients. Tracing out one subsystem implies that the other subsystem is mixed. ...
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Baker-Campbell-Hausdorff (BCH) Formula for the Time Evolution Operator

In following Prof. Toyer's Computational Quantum Physics lecture notes, I came across the following: In computing the Schrödinger equation in real space, one can make a "split operator" Ansatz, for ...
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279 views

$2s\rightarrow 1s$ transition in hydrogen

I would like to understand how the parity-violated interaction between electron and proton can provide the photon with circular polarization in the $2s\rightarrow 1s$ transition with single photon ...
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1answer
81 views

Wave function evolution of an electron [closed]

In many basic quantum mechanics books the wave packet of an electron is described. It will say that the wave packet will broaden as time evolves because of dispersion. But suppose the electron just ...
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Does uncertainty principle truly represent the “lower bound” of the information we can obtained from a pair of noncommunicable operator?

Background I: Suppose the commonly used non commuting operator $\hat p$ and $\hat x$. The uncertainty principle told us that $\sigma_p\sigma_x\geq \frac{\hbar}{2}$. In standard quantum mechanic ...
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What's the difference, if any, between Soft Hair & Quantum Hair

In the early 90s, John Preskill, Sidney Coleman, Frank Wilzcek and Lawrence Krauss presented a series of papers [1][2][3] on Quantum Hair on Black Holes due to Cosmic strings in a number of ways ...
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Why is the ground state of a particle in a box called $n=1$?

For a quantum harmonic oscillator, the ground state in most sources is referred to as $n=0,$ and this state has zero nodes. For a particle in a box, the ground state in most sources is called $n = 1.$...
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Relativity and Quantum Mechanics

I have been thinking about the problem of relativistic path integrals and I encountered several difficulties. Let's assume we have a particle initially a position $x_i$ at $t_i$ in a certain reference ...
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Why is there a factor of $\sqrt2$ listed for the neutral pion?

I was reading the Wikipedia page on pions. At the bottom of the page, there is a listing for the neutral pion ($\frac{\rm u\bar u+d\bar d}{\sqrt{2}}$). Why are they over the square root of 2? There ...
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When is separating the total wavefunction into a space part and a spin part possible?

The total wavefunction of an electron $\psi(\vec{r},s)$ can always be written as $$\psi(\vec{r},s)=\phi(\vec{r})\zeta_{s,m_s}$$ where $\phi(\vec{r})$ is the space part and $\zeta_{s,m_s}$ is the spin ...
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How can I prove that the partial trace is well-defined?

When I define the partial trace as below, how can I prove it well-defined? I understand that I have to indicate $Tr_k(\rho)$ does not depend on how to take the ONB of $\mathbb{C}^2$ $$n\in \mathbb{Z}_{...
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Does the measuring instrument which counts the number of quantum particles exist?

I have recently been thinking about the quantum deletion error correcting codes, but the primary problem is whether the receiver can detect the loss of quantum particles or not. So my question is that ...
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Relation between the position operator and the Berry connection

If I write the position operator $\hat{x}$ as $i\frac{\partial}{\partial k}$ and act it on the Bloch state $|u_k>$, I get $<x>=i<u_k|\frac{\partial}{\partial k}|u_k>$. This is the same ...
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What rules have been proposed for hidden variables? [closed]

I am not asking if hidden variables are possible. If pairs of photons are produced with mirror image momentums and matching polarization what additional variables have ever been proposed? Where are ...
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How do I know whether the description of an electron state is complete?

Let's consider an electron as part of a larger system as an atom consisting not only of a nucleus but also of several other electrons. I guess, one can characterize the atom quantum-mechanically in a ...
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190 views

Schmidt decomposition - example

I'm trying to compute the Schmidt decomposition of $\left| \psi \right> = (\left| 00 \right> + \left| 01 \right> + \left| 10 \right>)/\sqrt{3}$. This should be possible by first computing ...
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Rydberg Blockade's experimental mechanism

This idea for an experiment is for a high school competition (bl4s). Utilizing a positron beam,can we knock out gas which has been energized to its Rydberg state.I plan to do this to verify when the ...
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The products of powers of Hermitian operators

Let's say I have two operators, $\hat{x}^k$ and $\hat{p}_x^l$, where $\hat{x}$ and $\hat{p}_x$ are the ordinary position and momentum operators. It seems fairly straight forward to show that $\hat{x}^...