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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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QM: Why is the geometric phase not zero?

I'm studying the adiabatic theorem and there is a derivation of a geometric phase factor which incorporates terms of the form $\langle \dot \psi_n (t) | \psi_n (t)\rangle$ where the $\psi_n(t)$ are ...
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Klein-Gordon Inner Product from Greiner's book doubt

I was working on free field theory from Greiner's book "Field Quantization" In chapter 4, he introduces these phase functions: $$ u_{p}(\boldsymbol{x}, t)=N_{p} \mathrm{e}^{-\mathrm{i} p \cdot x}=\...
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40 views

Change of basis in the many worlds interpretation?

Say we have two orthogonal states $|A\rangle$ and $|B\rangle$. In the many worlds interpretation, we can imagine two parallel universes in which we are either in state $A$ or $B$. But now if we ...
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How to plot Majorana energies for Kitaev chain as function of mu?

My first attempt was, using the Python library Kwant, getting the lowest eigenvalues for the 1D p-wave superconductor as a function of the chemical potential mu (In the image below I show what I got). ...
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Photon creation operator physical realization

I am trying to self study QED so I apologize if my question seems silly. As I realize, all physical processes should stem from some "hermitian" operator in the quantum language. As it is well known, ...
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2answers
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Are there more than 3 dynamical pictures of quantum mechanics?

There are 3 well known dynamical pictures of quantum mechanics: the Schrödinger picture, the Heisenberg picture and the interaction picture. In above wikipedia article, their connection is nicely ...
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Interaction picture counter rotating terms

In the interaction picture, we often do the rotating wave approximation where terms like $e^{i(\omega_1 + \omega_2)t}$ are ignored because they represent rapidly oscillating terms which ends up ...
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4answers
100 views

Cheap classroom demonstrations of quantum mechanics

In a few weeks I'm going to be teaching a week-long class on quantum mechanics at a summer program for very mathematically talented high school students. I'm planning to focus on the finite-...
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Hamiltonian in Piers Coleman - Introduction to Many-Body Physics book

In the book "Piers Coleman - Introduction to Many-Body Physics (2016, Cambridge University Press)" in page 491 When an electron pair is created, electrons can only be added above the Fermi ...
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Does Quantum Mechanics claim that dynamical fields have quantum properties?

While reading some of the non-technical articles on quantum gravity, I have come across to a message several times. Consider the following quote taken from the articles form "Approaches to Quantum ...
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Would this experiment disprove/prove that consciousness causes collapse?

A double slit experiment, is taking place. There are detectors, placed inside both of the slits. On the first run if a particle travels through one of the slits, the detector registers, that it has ...
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A doubt about a naive generalization of inner product in elementary quantum mechanics

A elementary study of Quantum Mechanics, following $[1]$, yields in the realization that the basic algebraic structure are the complex vector spaces $\mathbb{C}^{n}$. Then a contravariant vector (...
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Does this thought experiment proves that Standard Quantum Mechanics and Pilot Wave Theory make different predictions?

Here is a thought experiment that is supposed to show that standard quantum mechanics and pilot wave theory do not make the same prediction : Take the double slit experiment, and add a detector in ...
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Berry connection in a solid

I am having troubles to understand an equation-sign for the Berry connection in a solid. The general formula reads \begin{equation} \vec{A}(\vec{R}) = \mathrm{i} \langle \Psi(\vec{R}) \, | \nabla_{\...
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Berry Curvature in a hexagonal lattice

I am having troubles to understand the concept of the Berry curvature in a hexagonal lattice. What I know is: The Berry curvature $\Omega_n (\vec{k})$ for the $n$-th band reads \begin{equation} \...
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40 views

Calculating exact energy levels of perturbed Hamiltonian

I wish to find the exact energy levels of the following perturbed hamiltonian. $$\hat{H}=\frac{p^2}{2m}+\frac{m\omega^2}{2}x^2+\alpha x+\beta p^2.$$ I believe that it can be solved by using the ...
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Finding eigenvalues and functions for Hamiltonian (perturbation theory)

I am trying to find the Eigenvalues for the following equation (which comes from the Pauli equation when $p^2/m^2c^2\ll 1$): $$i\hbar\frac{d}{dt}\psi=\left[\frac{\vec{p}^2}{2m}-\frac{e}{2mc}\left(\vec{...
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Is this analysis contradictory with the $2$'nd measurment?

Summary and Motivation "The below idea is about making a mathematical statement on system $2$ which induces a measurement on system $1$ while $1+2$ obeys unitary evolution." Introduction There are $...
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Distance of two indistinguishable particles

Consider: The wavefunction of a two-particle system (both Fermions and Bosons possible): $$ \psi_\pm(x_1,x_2) = \sqrt{\frac{1}{2}}[\psi_n(x_1)\psi_m(x_2) \mp \psi_m(x_1)\psi_n(x_2)] $$ And a ...
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What is the derivation of the wave guiding equation in Bohmian Mechanics?

I've been looking around the internet for a proof of the waveguiding equation in Bohmian mechanics but I can't find one anywhere. I know that Bohmian Mechanics is a frowned upon theory, but it hasn't ...
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48 views

Finite potential well; finding the energy “in a limit”

I've come a across the following variant of the finite-potential-well-problem in quantum mechanics: The potential is given by $V(x)=0$ for $|x| \geq a/2$ and $V(x)=-V_0/a$ for $-a/2<x<a/2$ where ...
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What importance of battery “ voltage” between cathode and anode in photocell? [duplicate]

In photocell at threshold frequency $f=f_0$ and voltage $>0$ (between cathode - and anode +) Is current $=0$ at $f=f_0$ and $v>0$? When voltage $>0$ and $f=f_0$, Does photoelectron have KE ...
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How everyone can benefit from learning physics? [on hold]

What would be benefits of learning physics in a relatively rigorous way (meaning to take a quick look even at the topics that are more advanced, like quantum field theory) for people who don't aspire ...
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If there are eigenstates of $L_z$ in a degenerate subspace, are there also eigenstates of $L^2$?

The question arises from an exercise but tackles deeper understanding of angular momentum operators. Suppose we have a 2D harmonic oscillator and an infinite square well in the third dimension: \...
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Why must momentum operator in infinite well be self adjoint?

First, let me preface this statement by saying I know that there exists no (unique) self adjoint extension of the standard differential operator for the space $L_2([0,1])$. However, when one attempts ...
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Block universe and quantum mechanics [duplicate]

Can a block universe (complete determinism) ever be compatible with quantum mechanics?
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3answers
61 views

Which particle mediates the Aharonov-Bohm effect?

BACKGROUND The Aharonov-Bohm (AB) effect induces phase shifts between the two paths that an electron could take around an enclosed magnetic field. In radial coordinates, assume that the magnetic ...
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How should two-photon transitions be modelled? Is second-order perturbation theory required? Or are sequential first-order processes sufficient?

For example, I want to consider the following situation: photon transit from $m$ energy level to $m+2$ after absorption of two phonons with frequency $\Omega$. I want to calculate a transition rate ...
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1answer
36 views

Creation and Annnihilator Operators: generality and meaning

I am studying my fisrst course in quantum mechanichs where we treated the example of the Harmonic Oscillator through the Weyl Heisenberg Spectrum Generating Algebra Method. In that context we ...
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1answer
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What does it mean to say “since the magnitude of actual momentum is smaller than uncertainty, the value cannot be defined”?

What does it mean to say "since the magnitude of actual momentum is smaller than uncertainty, the value cannot be defined"? Original question: Uncertainty in the momentum of an electron is $ 2.6 \...
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1answer
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Quantum mechanics limits to understanding the Universe [on hold]

By definition, a wave function does not describe a particle's state exactly, we can only know that information when we make measurements and thus collapse the wave function. This gives us a lot of ...
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1answer
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Diffraction pattern of X-ray and electron

Electron diffraction is used to study about wave - particle duality of matter. A beam of electrons directed at a single crystal produced a diffraction pattern like an X-ray diffraction pattern. I ...
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Is there a maximum quantum advantage in sensing?

This is a rather conceptual question. Quantum sensing takes advantage of entanglement (and other quantum properties such as squeezing) to get variances that scale much better than the ones one can ...
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Is quantum energy uncertainty underestimated in liquid molecules?

Liquids have the molecular property that the collision frequency (collisions per time) among the molecules is extremely high; it is at the order of picoseconds. Consequently, the Quantum uncertainty ...
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How to approximate electron electron interactions in helium Hamiltonian?

So I know that using the helium Hamiltonian has no analytic solution in the SE. I'm wondering how one goes about approximating the solution.
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Expansion of Von Neumann entropy for small deviations

Suppose that your quantum system is described by $\sigma = \rho + \delta\rho$, where both $\sigma$ and $\rho$ are density matrices while $\delta\rho$ is "small". The Von Neumann entropy of the system ...
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Diagonalisation of quasi-thermal state

I have the following density operator $$\frac{1}{t \pi N} \int_{\mathbb{C}} \mathrm{d}^2\gamma \exp \left[ -\frac{|\gamma+r\alpha|^2}{t^2 N} \right] |{\gamma}\rangle\langle{\gamma}|,$$ where $0\leq t,...
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Why are these two variables being treated differently in the action?

I'm trying to understand the derivation provided in the section 2.4 of this paper. I have modified the notation and cut out the unimportant parts of the equations for clarity purposes, but for ...
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If a particle can exert a force on itself,then can we define a whole lot of newtonian mechanics corresponding to it?

I think that it may be a broad question to be answered but if small amount of discussion is possible then it would be very helpful for all of us. Basically,I asked a question on this website a few ...
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How can I calculate the hyperfine structure of a $p$-orbital?

I have a little problem with the calculation of the hyperfine structure of the 3p orbital in the hydrogen atom. The Hamiltonian is: Were represents the magnetic moment of the proton and the ...
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1answer
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Finding the eigenfunctions of the operator $x$

On pg 104 of "Introduction to Quantum Mechanics" by Griffiths, we are asked to find the eigenfunctions of the $x$ operator. Hence, we have to find functions such that $$x f(x)=\lambda f(x)$$ I have ...
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Confusion regarding $|A|^2 \int\limits_{-\infty}^\infty e^{i(p-p')x/h}=|A|^2 2\pi h\delta(p-p')$ [migrated]

The book "Introduction to Quantum Mechanics (Second edition)" by Griffiths says the following on pg 103: $$|A|^2 \int\limits_{-\infty}^\infty e^{i(p-p')x/h}=|A|^2 2\pi h\delta(p-p')$$ Here $\delta$...
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Having some issue with notation in a Hilbert space

What is the difference between these two? $\langle x|x\rangle$ and $|x\rangle\langle x|$ Are they the same? If they're the same, why are they used in these two different forms?
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2answers
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Contour for integration in 1D scattering problem

A plane wave scattered by a 1D potential can be described by, $$\psi(x) = \begin{cases} e^{ikx} + R e^{-ikx}, & x<0\\ T e^{ikx}, & x>0 \end{cases}$$ where $R$ is the reflection ...
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Field operators and “the source” term

So, in a book on QFT there is in the begining some talk about Klein-Gordon field and equation. This is solved by using simple harmonic oscilator formalism and a spectrum for a free H is found. But ...
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Is photocell current equal zero at threshold frequency?

In photocell is there currant at threshold frequency $f=f_o$? I mean $I=0$ at $f=f_o$?
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Harmonic oscillator path integral: regularizing the functional determinant

From Polchinski's Vol. 1 Appendix A, we can reduce the Euclidean path integral for the 1D harmonic oscillator to computing $(\det\frac{\Delta}{2\pi})^{-1/2}$ where $$\Delta = -\partial_u^2 + \omega^2.$...
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Proper time for a relativistic particle in quantum mechanics?

It is an often cited fact that a muon falling through the atmosphere at great speed has a decay time longer than the one we would observe in the same particle at rest due to relativistic effects, and ...
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Signal coherence/correlation vs quantum coherence

In general, I understand a signal $s(t) \in \mathbb{C}$ is called "coherent" when it has a large autocorrelation function. A pair of different signals $s(t)$, $r(t)$ can also be "coherent" if their ...
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Dirac spinor as null vectors

In this paper, on page 9, the authors show that a spinor is equivalent to a null vector with a bit of extra structure (just one real parameter I think?): https://arxiv.org/abs/1312.3824 They then go ...