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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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Wave-like properties of particles [duplicate]

If we consider a particle such as an electron to have wave-like properties too, what kind of wave it is? What is exactly meant by its wavelength?
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1answer
71 views

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 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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1answer
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How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule?

How to obtain the quantization of a simple pendulum using Bohr-Wilson-Sommerfeld rule?
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2answers
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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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3answers
33 views

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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39 views

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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1answer
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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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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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1answer
46 views

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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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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'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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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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1answer
58 views

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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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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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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0answers
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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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1answer
27 views

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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1answer
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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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1answer
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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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0answers
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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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0answers
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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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4answers
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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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1answer
51 views

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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26 views

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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0answers
25 views

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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5answers
77 views

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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1answer
18 views

Self consistent calculations in quantum well. Mixing by electron density?

I'm challenging the problem of calculating energy structure of InAs/GaAs quantum well. One part of the task is to perform self consistent calculations in order to include potential that comes from ...
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1answer
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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 ...
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1answer
60 views

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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23 views

Hawking radiation inside a black hole [duplicate]

For a virtual particle pair is produced within the horizon, a mass of black hole decreased from the negative energy particle into the black hole or the positive-energy particle tunnel away from the ...
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0answers
51 views

Expression for $p^4$ in quantum mechanics [on hold]

In Griffith's Quantum mechanics,he asks to show that $p^4$ is not hermitian. Now I am stuck at what should be expression for $p^4$ in this question. Any hint?
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Is light and darkness,negative & positive a part of one all encompassing force? [on hold]

Is light and darkness negative & positive both part of the same all encompassing Reality (Force),they both being a part of this reality(this universe),& reality(this universe)being one thing,...
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How to interpret overlap in Hamiltonian if it is not a degeneracy?

In Fruchart et al.'s An Introduction to Topological Insulators, the Bloch Hamiltonian for a two-band insulator is given in the general form $ H(k)= $ \begin{bmatrix} h_0+h_z & h_x-i h_y \\ ...
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1answer
43 views

Eigenvalues of the Hamiltonian

Is every eigenvalue of the Hamiltonian a form of energy? If not are there values of the Hamiltonian that do not correspond to the energy of the system?
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31 views

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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1answer
47 views

Physical understanding of the 'box' in quantum mechanics models [on hold]

Few classic quantum mechanic models will be particle in a box (infinite depth), particle in a box (finite depth), harmonic oscillator (HO) and mechanical rotation (MR). The wave functions of a QM-HO ...
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1answer
29 views

Do topological transitions only occur at Dirac points?

Topological phase transitions happen when the band gap closes. It is not true that all band crossings are topological. There are Dirac (linear) band crossings, quadratic band crossings, Dirac-like ...
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1answer
28 views

Decay of spin-1 particle into two spin-0 particles

If we consider the decay of a spin-1 particle with spin projection $m_s=1$ into two (distinguishable) spin-0 particles, what are the possible values of the orbital angular momenta $l$ of the resultant ...
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1answer
34 views

Is there a simple way to numerically solve interacting fermion systems like for spins?

I know that if one has a spin chain of N spins, with the interaction described by some Hamiltonian, one can find the eigenstates and energies by using Kronecker products to write the Hamiltonian as a $...
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1answer
53 views

What is “Rotational Invariance” in the context of qubits

In this question the state, $\frac{1}{\sqrt{3}}\left|00\right\rangle +\frac{1}{\sqrt{3}}\left|01\right\rangle +\frac{1}{\sqrt{3}}\left|11\right\rangle$, has been said in the answers to not be able to ...
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1answer
80 views

Lloyd's mirror problem [on hold]

My question is about the reflection of the interference pattern from the screen to the mirror itself in the(Image B), as you can see in the mirror the reflected interference pattern is similar to ...
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2answers
45 views

What happens when measuring a subsystem of a product bipartite state?

I have an horrible doubt, as I found that in my books the question is never directly addressed. How is collapse defined to work for measures of composite system? I always assumed that when we ...
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0answers
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What is the high-energy/superstring analogue of wave function?

Chapter 12 of Beckers' book about superstrings and m-theory lists several deep dualities between low energy gauge theories and high energy superstring theories. I am only at the Chapter 2, that is why ...
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Can someone give a lay explanation why the 'quantum mechanical limit' should not exceed 2√ 2? [on hold]

I read in a few papers, such as the 2018 Rauch et al. paper, that assuming a quantum mechanical explanation the probability of a correlation should not exceed 2√2. Can someone explain in lay terms ...
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0answers
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Biconformal space and curvature

I've found very few contributions about the so called Biconformal Space, "a curved phase space". I was sure that in general phase spaces are cotangent bundles naturally equipped with a symplectic 2-...
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2answers
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Interpretation of the energy-time uncertainty [duplicate]

From the uncertainty relation it follows that: $$\Delta E \ \Delta t = \hbar$$ $\Delta E$ is the energy uncertainty of a state, $\Delta t$ should be the uncertainty of the lifetime $\tau_b$ of the ...