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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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Time units in simulation

I am hoping that someone could give me some insight about my problem. Currently I want to simulate the evolution of a gaussian wavepacket in a time-dependent potential using the Crank-Nicolson scheme. ...
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General derivative of the exponential operator w.r.t. a parameter

I am interested in the calculation of the general $N-th$ derivative w.r.t. a parameter $\lambda$ of a quantum mechanical exponential operator with the following structure: \begin{equation*} \frac{\...
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How to interpret this construction of the states in QFT?

Non-Relativistic Quantum Mechanics To make this question clear it might be useful to contrast with non-relativistic quantum mechanics. In any quantum theory, the states of a system are unit rays in ...
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how spinfull chains in 1d are possible since spin is not well defined in 1d?

as far as I know, in QM spin is not defined in 1d, because of algebra$\mathfrak{su}(2)$ can not be satisfied in 1d. however we talk about spin chains, spinfull luttinger liquids in 1d all the time. I ...
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harmonic oscillator position expectation value

I'm trying to get the expected value as a function of time for the position, of a harmonic oscillator hamiltonian and a state vector $|\psi\rangle=a|0\rangle+b|2\rangle$. I have $$|\psi(t)\rangle=...
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Can a particle be physically observed inside a quantum barrier?

I understand that if a particle approaches a finite potential barrier of height $V_0$ with energy $E < V_0$, there is still a finite probability of finding the particle on the other side of the ...
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Could a non-unitary time evolution violate the no-cloning theorem?

It is written in some places that the unitarity of time evolution is what prevents quantum cloning. However, consider the typical definition of a cloning operator $A$. For all $\left|\psi\right>$ ...
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Is the Moyal-Liouville equation $\frac{\partial \rho}{\partial t}= \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]$ used in applications?

This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form $$ \frac{\partial \rho}{\partial t}~...
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quantum eraser question

I have a question concerning the quantum eraser: Let's assume you have two envelopes with one having the printed detector data and the other one having the printed measurement screen data, for a ...
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Energy formula for finite potential well [on hold]

The energy formula for infinite potential well is $$E=\frac{n^2h^2}{8ma^2},$$where $m$ is the mass of the particle, $a$ is the width of the well but in the case of finite potential well, I actually ...
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Interaction picture: why the Hamiltonian describing the dynamic doesn't change with the same law as other observables?

First: what happens in a general change of picture? If I have the following equation: $$ A | x \rangle = | y \rangle .$$ To do a change of picture is to apply a unitary $U$ on all vectors of the ...
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Impact of electronic binding energies on mass and acceleration

According to relativity, the inertial mass of an object that enters into the force equation to get acceleration is given by the total energy in the center of mass rest frame. $$E=Mc^2=\sum_i (m_i c^...
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What is the physical meaning of time-averaged Hamiltonian?

I saw in the literature related to the systems with periodic driving forces, people often define a "time averaged Hamiltonian" as $$H_{\text{avg}}=\frac{1}{T}\int_0^T H(t) \ dt.$$ But I do not ...
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What is line broadening phenomenon in quantum many body physics?

I have been reading Anderson's paper, "Absence of diffusion in a certain Random Lattice" and found the concept of inhomogeneous broadening. I couldn't really find a satisfactory explanation with a ...
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Particle in a box - speed probability distribution

Consider a particle in a box with infinite barriers. By solving the Schrödinger we can find the probability of finding the particle at some points in the box. How can we find the probability of ...
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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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Why do atoms emit a certain colour of light? (The emission spectra)

We were taught about the emission spectra in class last year, but my teachers couldn't give me an answer to 'what determines the colour of light emitted?'. (they were giving me the answers to the ...
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Bound states, scattering states and infinite potentials

I am doing my first semester of Quantum Mechanics and we're using Griffith's Introduction to Quantum Mechanics. As he is introducing the Dirac delta function potential he explains bound and scattering ...
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Is there a relation between the factorisation of the joint conditional probability distribution and Bell inequality?

I'm approaching the study of Bell's inequalities and I understood the reasoning under the Bell theorem (pdf : https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf) and how the postulate of ...
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'Show that $E$ must exceed $V(x)$ for every normalisable solution of the TISE'. Surely you can show that this isn't true using exponentials?

In Griffith's this is a question, there's the clear answer which jumps out immediately: $$\frac{d^2\psi}{dx^2} = \frac{2m}{\hbar^2}(V(x)-E)\psi.$$ That is, if E is less than V the second deriviative ...
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Question regarding Little group for massless particle

Consider a particle with velocity $P = (1,1,0,0)$. The little group for it is E(2) (same as). Here, in this book by YS KIM, he talks about this little group in section 2.3. He says in addition to E(2)...
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What is the nature of vibrational relaxation in fluorescence?

Electrons in fluorescent substances get excited from the ground state($S_o$) to the first excited state($S_1$) or higher excited states in case of upconversion. Depending on the statistical ...
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What is the variance of |S| in Bell's inequality (CHSH inequality)

Sorry that this isn't a quick question but I didn't know how to make it shorter. I am struggling with this for quite a long time and I would appreciate every help that I can get. I could not find a ...
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1answer
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Does Bell's theorem imply nonlocality using a false assumption?

In https://arxiv.org/abs/1409.5158, the author concludes that Bell tests cannot refute local realism, because they employ a wrong analysis. He says: "The quantum joint prediction cannot be ...
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Harnessing molecule vibration energy

Disclaimer: I am learning physics for fun, please dont kill me but explain where I am wrong. As I understand all molecules have a lowest energy state in which they posses some amount of momentum even ...
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Can the total energy of a solid be measured with photoemission?

Angle resolved photoemission spectroscopy (ARPES) is a really popular tool developed to study the behavior of solids by looking at the behavior of their photorlectrons. This is used to measure ...
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How looks the “overarching” wavefunction of a number of electrons in an insulating sphere?

I changed my question after reading the comment of Anna. If we put a huge number of electrons inside a non-conducting sphere, what will the total wavefunction describing all electrons look like? I ...
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Reality, locality, and universality in the EPR paradox

Apologies if this has been asked before. I did some searching but didn't see it anywhere asked quite like this. Thanks in advance for any insights. Caveat: I am an organic chemist and thus ...
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Orthonormal basis written in Dirac Notation

$\left\{ e _ { i } \right\}$ is an orthonormal basis which has the orthonormal condition as following: $$e _ { i } ^ { T } \cdot e _ { j } = \delta _ { i j }$$ In Dirac Notation where $| i \rangle = | ...
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Operational Equalities [on hold]

How to check the following operational equalities: $$ x^2\dfrac{d}{dx} \dfrac{1}{x}=x \dfrac{d}{dx}- 1 \quad \& \quad \left( x +\dfrac{d}{dx} \right)^2= 1 + x^2 +2x\dfrac{d}{d x} + \dfrac{d^2}{d ...
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Discretization of Hamiltonian with first derivative

In a particular 1D system, the Hamiltonian can be writen as $$H=\mathrm{i}\left(f(r)\frac{\partial}{\partial r}+\frac{1}{2}f'(r)\right)\; ,$$ wher $\mathrm{i}$ is the imaginary unit, and $f(r)$ is a ...
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What is the angular momentum of an electron? And how can it be zero?

I'm in my first undergrad physics series and we're learning a bit about quantum mechanics. We've been studying the hydrogen atom in it's ground state. We're using the time independent Schrodinger ...
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How wave functions overlap in STM

In STM(Scanning Tunnelling Microscopy), as distance between tip and sample decrease tunnelling current increases. I know that when it cross barrier wave function decay exponentially. Measured current ...
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How to find energy levels formula for symmetric triangular potential well [on hold]

As some of you already know that the asymmetric triangular potential well has the energy level where an here refers to the airy function a1 =2.338, a2=4.088, a3=5.521 and a4= 6.787 and V=eFz (F here ...
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What is the definition of colour (the quantum state)?

I heard somewhere that quarks have a property called 'colour' - what does this mean?
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Derivative with respect to perturbation in QM

The book "Introduction to Computational Chemistry" by Frank Jensen claims the following (Eq. 10.35): Let $H(\lambda) = H_0 + \lambda V$ be a Hamiltonian parametrized by a perturbation strength of $\...
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What is the difference or connection between inverse proximity effect and triplet proximity effect in superconductors?

I know that inverse proximity effect affect the order parameter of the superconductor and that triplet proximity effect convert singlet Cooper pairs into triplets. But how is the two phenomena ...
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How to chose which formula to use for thermal energy?

In some cases we use (3/2)kt in some cases kt and some cases (1/2)kt. How to chose which formula to use for thermal energy?
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Derivation of density of states for a gas with $N$ states

I am trying to find any information on the derivation of the density of states for a system with periodic boundary conditions in 3D. I know how it works with 1 particle since I have seen the ...
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Eigenkets in Interaction Picture

Let us consider a system. In Schrodinger picture, its Hamiltonian $H$ is given by $H = H_0 + V(t)$, where $H_0$ is the unperturbed Hamiltonian and $V(t)$ is the time-dependent perturbation. In ...
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Liouville equation solution for the hydrogen atom

Has anyone done an analysis of the Coulomb potential problem (for example the hydrogen atom) from a probabilistic classical viewpoint using Liouville equations, and then contrasted this with the QM ...
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Entanglement and mass-energy [on hold]

Consider two systems of particles. They are identical systems except in one respect: In system A the particles are all entangled with one another, and in system B none of them are. Do A,B possess the ...
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Metric interpretation of self-adjoint extensions?

I am wondering if beyond physical interpretation, the one dimensional contact interactions (self-adjoint extensions of the the free Hamiltonian when defined everywhere except at the origin) have a ...
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Negative probabilities in quantum physics

Negative probabilities are naturally found in the Wigner function (both the original and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
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Why are Pauli vectors for different particles opposite in the singlet state?

If $\boldsymbol{\sigma_{1}}$ is the Pauli vector for a particle and $\boldsymbol{\sigma_{2}}$ for the other particle, why is $\boldsymbol{\sigma_{1}}=-\boldsymbol{\sigma_{2}}$ in the singlet state? I ...
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How does the Pauli exclusion principle apply to wave-particle duality?

Based on the Pauli exclusion principle , no two particles can have the same quantum state. However, in the double slit experiment with electrons (in which we observe wave-particle duality), at some ...
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Non-relativistic limit of particle decay

Let us consider the theory with scalar coupling $g\bar{\psi}\phi\psi$. For the decay process $\phi\rightarrow \bar{\psi}\psi$ one can write down the following amplitude: $$\mathcal{M}=ig\bar{u}(p_{-})...
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What is the difference between coherent states and the entangled states used in quantum illumination?

I've been reading about utilising quantum illumination systems to out perform classical microwave radars, but I've gotten confused over a point they're making regarding the distinction between the ...
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Reference Frames and the De Broglie Wavelength

If the de Broglie wavelength of a massive particle, is h/mv then doesn't that mean interference patterns and everything change their properties depending on the velocity of the observer? How can QM ...