All Questions
40
questions
0
votes
0
answers
63
views
What does it mean by "physical field"?
I'm attempting a question about the Stern-Gerlach experiment where an electron is used with an assumed up-spin state in a non-uniform magnetic field. It asks us to talk about the dynamics of this ...
- 11
-3
votes
3
answers
65
views
Help with forming a dimensionless combination proportional to $e^2$ [closed]
I am currently working on a physics problem that asks me to form a dimensionless combination of the fundamental constants $e=\left|q_e\right|$, $\hbar$, $c$, and $\epsilon_0$ that is proportional to $...
- 19
1
vote
1
answer
432
views
A difficulty in understanding "Kinetic Momentum" of A Charged Particle in a Magnetic Field
Maybe the title is not accurately stated.
There are few doubts about my question itself, these are-
Is Kinetic Momentum an operator?
I said "A Charged Particle", not "A Moving Charged ...
0
votes
1
answer
69
views
How can I construct linear polarization states of a photon from circular polarization states?
I'm a second-year math student and one of the courses is physics. We just started quantum mechanics, and the lecturer briefly explained the Bra-ket formalism and gave us students the following ...
- 43
0
votes
2
answers
175
views
Building Lagrangians for Classical Field Theory
I've been studying quantum mechanics and classical field theory for quite a while now. However, I still struggle with the idea of building scalars from vectors and tensors for the Lagrangian density.
...
- 1
2
votes
2
answers
121
views
Wave equation solution satisfied? [closed]
I'm having a problem trying to show that this solution satisfies the wave equation. I discovered this solution given by $$\psi(x,t)=e^{-(ax-bt)^2}$$ but I'm stuck trying to prove that solution ...
- 23
1
vote
0
answers
832
views
Density of States (DOS) to energy graph
I am trying to find the amount of electrons in a conduction band in Si (Silicon), all I've got is a graph similar to this one:
I've tried to integrate like this:
$$ N = \int_{1}^{\infty} \frac{1}{1+\...
- 11
0
votes
1
answer
101
views
Quantum mechanics. Scattering from step potential barrier of magnetic field
I am having trouble to think how to solve the following problem:
The plane $x=0$ separates two parts of space: when $x>0$ there is homogeneous magnetic field, which induction vector $B_x=B_y=0$, ...
- 47
2
votes
1
answer
447
views
Landau levels in rotationally invariant gauge
I try to find wave-function of electron in external constant magnetic field in gauge
$$A=\frac{B}{2}(-y,x,0).$$
I substitute anzats, $\psi=e^{-i\omega t}e^{ip_zz}F(x,y)$. Then, I rewrite equation in ...
- 2,654
2
votes
1
answer
133
views
Problem in deriving Pauli equation
I’m trying to derive the equation from the Hamiltonian
$$H=\frac{1}{m}[\vec{\sigma} \cdot (\vec p-q\vec A)]^2+ q \phi$$
and
$$[\vec{\sigma} \cdot (\vec p-q\vec A)]^2= (\vec p-q\vec A)^2-iq \vec{\...
- 483
3
votes
1
answer
5k
views
How do we derive the minimal coupling Hamiltonian?
Is there a way to rigorously derive the minimal coupling hamiltonian for a system interacting with electromagnetic radiation. How de we arrive at the expression:
$$\hat{H} = \frac{1}{2m}(p-\frac{q}{c}...
- 352
1
vote
1
answer
131
views
Wigner-Weyl transformation for particle in magnetic field
I consider particle in external magnetic field, ${\bf A}=(-yB,0,0)$ and find wave functions (may be up to normalization factors),
$$\psi(x,y,z)=\sum_n\sum_s\int\frac{dp_xdp_z}{(2\pi)^2}f_s\left(eBy+...
- 2,654
1
vote
0
answers
22
views
Does the absorption intensity for vibrational transition depends on the angle between the electric field vector and the transition moment vector?
Is the transition possible even if there is a certain angle between the electric field vector and the transition moment, given that the photon and molecule are in resonance. My notion is that the ...
- 21
12
votes
2
answers
7k
views
Proving Gauge invariance of Schrodinger Equation
I am trying to proof explicitly that Schrodinger equation:
$$ i\hbar \partial_t \psi = \left[ -\frac{1}{2m}\left(\frac{\hbar}{i}\nabla-q\vec{A}\right)^2+qV \right]\psi$$
remains the same under the ...
- 980
1
vote
2
answers
686
views
Eigenvalues dependent on choice of $\vec{A}$? (Pauli hamiltonian)
I found in this article a straightforward way to calculate the eigenvalues of the hamiltonian of an electron under the influence of an homogenous magnetic field (p. 5): http://www.phys.spbu.ru/content/...
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