All Questions
21
questions
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Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set? [closed]
Copy from here https://mathematica.stackexchange.com/questions/284809/why-does-the-minimum-eigenvalue-change-dramatically-when-one-basis-function-is-a
I have a basis set which describes with high ...
- 233
1
vote
2
answers
480
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Series expansion of unitary operators in terms of other operators
I am reading lecture notes on local gauge invariance, part of Prof. Ethan Neil's course on Quantum Mechanics at the University of Colorado.
There, he writes about introducing a so-called comparator $U(...
1
vote
1
answer
121
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Expectation value of $ Y \otimes I \otimes I $ for a charged particle in a magnetic field
Typically when solving a Hamiltonian of ye olde form $ \frac{1}{2m} (\bar P - \frac{q}{c} \bar A)^2 $, you do separation of variables.
For simplicity say that $ A = - B Y \hat x $.
You can rewrite it ...
- 182
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votes
1
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51
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How to prove that momentum eigenstates are also eigenstates of asymmetric Landau Hamiltonian?
$$H(B,E)=\frac{1}{2m}p_x^2+\frac{1}{2m}\left(p_y-\frac{q}{c}Bx\right)^2-qEx$$
This Hamiltonian commutes with $p_y$, therefore, $\langle y|k_y\rangle=e^{ik_yy}$ are eigenstates of $H$, but how can I ...
- 97
5
votes
1
answer
287
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Is there a (semiclassical) electric field operator?
So I come from a chemistry background, where the electronic structure of atoms and molecules is central. For practical purposes, we usually work with a charge density operator
$$ \hat{\rho}(r) = q \...
user312272
0
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1
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127
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Ehrenfest theorem: On which classical circle can we find the electrons in an homogenous magnetic field?
In the French wiki article about the Ehrenfest theorem I found these formulas.
$${\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\langle {\hat {x}}\rangle ={\frac {1}{m}}\langle {\hat {p}}\rangle }...
- 708
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Quadratic Expansion With Operators [duplicate]
I was looking at the hamiltonian of a particle confined to the $x$-$y$ plane when it has mass $m$ and charge $q$ coupled to the electromagnetic field. My question is actually a very simple one. During ...
- 43
2
votes
2
answers
595
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How to understand the time reversal symmetry of position operator?
How to understand the fact that position operator is symmetric under time reversal? I can visualize the momentum and magnetic field being odd under time reversal.
Got the same doubt for Electric field ...
1
vote
1
answer
341
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Minimal coupling Hamiltonian
A charged particle in an em field can be described by the following Hamiltonian (in CGS units):
$$H = \frac {(\vec{p} \ + \frac {q}{c}\vec{A})^2}{2m} + U(r)$$
But... what does it mean to square the ...
- 1,644
2
votes
1
answer
170
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How to prove that the normal mode eigenvalue problem constitutes that of a Hermitian operator?
I am physics PhD student working on quantisation of electromagnetic fields in a non-homogeneous media. I am working through a paper at the moment and I am struggling with one of the statements. In the ...
1
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0
answers
56
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Why is there an inconsistency between the gauge transformation of the classical canonical momentum and the momentum operator in quantum mechanics? [duplicate]
I feel that there is a little inconsistency between the canonical momentum of a
classical charged
particle in an electromagnetic field and the momentum operator associated to the equivalent quantum ...
- 31
1
vote
1
answer
149
views
Schrödinger equation for charged particle in potential
This might be a silly question, but I don't think it is trivial.
I am trying to solve an example for my class. In it the Schrödinger equation for a charged particle in a vector potential is given:
$$i\...
- 1,488
0
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1
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98
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Evaluation of Hamiltonian of a charged particle under EM field
The Hamiltonian of a charged partical in EM field is given by $$H = \frac{\pi^2}{2m} -e \phi$$ where $$\boldsymbol{\pi}=-\mathrm{i} \hbar \boldsymbol{\nabla}+e \mathbf{A}.$$ To evaluate $\pi^2$, we ...
0
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1
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120
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Justification of dropping term in Hamiltonian and expectation Values
While reading Sakurai's Modern QM, I was stuck at the point where he explains the absorption and emission of light quanta in atoms. He proceeds with Hamiltonian:
$$H= p^2/2m + e\phi(x) -e/mc A\cdot p$...
- 129
7
votes
1
answer
580
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Why is the generalized momentum replaced by the momentum operator but not the ordinary momentum?
I was trying to understand the derivation of the Hamiltonian for a charged particle in an electromagnetic field. https://en.wikipedia.org/wiki/Hamiltonian_mechanics#...
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