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Results tagged with quantum-mechanics
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user 219318
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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Does the eigenbasis associated with an observable changes after measuring a different observ...
Suppose a system is initially in a superposition:
$$\psi(x) = \sum\limits_{i}|c_i\phi_i(x)\rangle$$
After a position measurement, the wave function collapses to one of the position eigenfunctions,$\ph …
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0
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One spin-1/2 particle in B field in a 3D harmonic potential (Part I)
Consider a spin-1/2 particle in a magnetic field (say in z direction) and in a harmonic potential. For the 3D harmonic oscillator component, The Hamiltonian $H_1= \frac{p^2}{2m}+\frac{1}{2}m\omega ^2r …
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One spin-1/2 particle in B field in a 3D harmonic potential (Part III)
Consider a spin-1/2 particle in a magnetic field (say in z direction) and in a harmonic potential. For the 3D harmonic oscillator component, The Hamiltonian $H_1= \frac{p^2}{2m}+\frac{1}{2}m\omega ^2r …
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Accepted
Why energy eigenstates form orthonormal basis
The first important property of a Hermitian operator is that it only has real eigenvalues. Try show it yourself starting from the eigenvalue equation:
$$ \hat H \psi_n(x) = E_n\psi_n(x)$$
taking adjoi …
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1
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439
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Spin-1 particle polarization direction
For spin-1 particle, I don't quite understand how the following relationship is derived:
$$\left|+1\right>=-\frac{1}{\sqrt2}(\hat e_x+i\hat e_y)$$
$$\left|0\right>=\hat e_z$$
$$\left|-1\right>=\frac{1 …
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Three operators commuting with each other
Yes. For example, when calculating angular momentum of a hydrogen atom (ignoring fine structure or hyperfine structure), the eigenbases (which are described by spherical harmonics) are simultaneously …
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Diffracted Electrons vs Particulate Electrons (Collapsed): Is there an experimental differen...
I think this famous experiment of electrons building up an interference pattern one by one answers your question.
http://www.datadeluge.com/2017/03/demonstration-of-singleelectron-buildup.html
When a …
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2
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How does magnetic monopole arise from Berry curvature?
The Berry connection is defined as
$$A_n(R)=i\left<\psi_n(R)\right|\nabla_R\left|\psi_n(R)\right>$$
and it is mathematically analogous to the vector potential.
We can then naively define the Berry c …
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0
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Examples of antiunitary operator other than time reversal operator
It is well-known that time reversal operation is implemented as an anti-unitary operator. I wonder what are some other examples of anti-unitary operators that appear in the context of quantum mechanic …
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Examples of antiunitary operator other than time reversal operator
Just for future reference, an example I encountered recently is the following: in the Bogoliubov-de Gennes (BdG) theory of superconductivity, the Hamiltonian has particle-hole symmetry. And the corres …
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Interpretation of induced force between two Dirac delta potential wells
My question is based on MIT OCW course 8.04 problem set 6 question 5(e).
https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/assignments/MIT8_04S13_ps6.pdf
Consider two Dirac delt …
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Infinite square well: wall with infinitesimal thickness
Given an infinite square well, it doesn't matter how thick the wall is, the particle is trapped inside the two walls. If we make the wall of arbitrarily small but finite thickness, the particle is sti …
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