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
440
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
176
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
837
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:
$$ N = \int_{1}^{\infty} \frac{1}{1+\...
- 11
0
votes
1
answer
101
views
Quantum mechanics. Scattering from step potential barrier of magnetic field
I am having trouble to think how to solve the following problem:
The plane $x=0$ separates two parts of space: when $x>0$ there is homogeneous magnetic field, which induction vector $B_x=B_y=0$, ...
- 47
2
votes
1
answer
448
views
Landau levels in rotationally invariant gauge
I try to find wave-function of electron in external constant magnetic field in gauge
$$A=\frac{B}{2}(-y,x,0).$$
I substitute anzats, $\psi=e^{-i\omega t}e^{ip_zz}F(x,y)$. Then, I rewrite equation in ...
- 2,664
2
votes
1
answer
134
views
Problem in deriving Pauli equation
I’m trying to derive the equation from the Hamiltonian
$$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+...
- 2,664
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
688
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/...
- 1,172
4
votes
1
answer
2k
views
How to solve the Schrödinger equation with magnetic field?
The Schrödinger equation of electron in a magnetic field is
$$
\frac{1}{2m} \left(-\mathrm{i}\hbar\nabla+\frac{e}{c}\mathbf{A}\right)^2 \psi + V\psi = E\psi
$$
where $V=-e\phi$ and $\phi$ is the ...
- 369
3
votes
1
answer
833
views
Symmetry in Landau's problem
Suppose a particle is forced to move in the $x-y$ plane, under a constant magnetic field $\vec{B} = B\hat{z}$. The Hamiltonian can the be written as
$$
H = \frac{\Pi^2}{2m}
$$
where $\vec{\Pi} = \vec{...
- 980
0
votes
1
answer
132
views
Retrieving the non-relativistic Hamiltonian from Relativistic QM
I'm trying to follow section 15.5 here, which derives the low-energy limit of the Dirac equation for an electron in a EM-field.
After some manipulations (which I think I follow alright) the author ...
- 253
-1
votes
1
answer
66
views
Aharonov-Bohm ring with many electrons
4 electrons are in an Aharonov-Bohm ring which the Hamiltonian is given by,
$$H=\dfrac {\hbar^2} {2mr^{2}}\sum _{n=1}^{4}\left( -i\dfrac {\partial } {\partial \theta_{n}}-4\right) ^{2}$$
How to ...
- 139
1
vote
2
answers
214
views
Any Rigorous Approach to Hydrogen Atom?
According to the book by David Griffiths on Quantum Mechanics, while solving the Schrodinger equation for the electron of Hydrogen atom, the Potential Function appearing in the Schrodinger equation is ...
user87745
0
votes
1
answer
521
views
Quantum mechanics by Griffiths, question on ch 10.2.3 (Aharonov-Bohm Effect)
I have just found this good site for Q&A on physics. What I want to question is about quantum mechanics written by Griffiths, Section 10.2.3 specifically, which is Aharonov-Bohm Effect.
According ...
- 3
2
votes
1
answer
88
views
Migdal's problem about rotating a particle in a magnetic field [closed]
I was given a problem by my professor, which belongs to Migdal. The problem is as follows:
If a particle is rotated by 2$\pi$ in a magnetic field its
wave-function $\psi$ transforms into $\exp(i\...
- 389
4
votes
0
answers
1k
views
Landau quantization: degeneracy of first level
In some books the degeneracy of one Landau level in a two-dimensional gas of free electrons is calculated in the following way:
Note: The electron spin is not considered.
Number of states of a free ...
- 171
1
vote
1
answer
188
views
Show the Berry phase is invariant under $U(1)$ unitary transform [closed]
Recall that $$\gamma_n = \oint A_n(R) \cdot dR = \oint \langle\psi_n(R)|i\nabla_R|\psi_n(R) \rangle \cdot dR.$$ Under the $U(1)$ transform, $$\psi_n \to \psi'_n \equiv e^{i\xi_n(R)}\psi_n,$$ where $\...
- 476
12
votes
1
answer
3k
views
Lorentz force derivation in quantum mechanics [closed]
In Sakurai and Napolitano, chapter 2, there's a derivation of the QM Lorentz force.
Given $$H=\frac{1}{2m}\left(\mathbf{p}-\frac{e\mathbf{A}}{c}\right)^2+e\phi = \frac{\mathbf{\Pi}^2}{2m}+e\phi$$
...
- 877
1
vote
0
answers
443
views
Landau levels in uniform magnetic field
Intro
Landau levels are obtained by gauging the vector potential to be
$$
\vec{A}=\left(-By,0,0\right)
$$
By which the Hamiltonian:
$$
H={1\over 2m}\left(\vec{p}-q\vec{A}\right)^2
$$
can be ...
- 695
1
vote
2
answers
189
views
Electropermanent Magnet not working?
I have made an electropermanent magnet based on summary provided on this blog.
Here are my details -
I have used AlNiCo and Neodymium Magnet together in the core with 10mm diameter and 20mm length.
...
- 121
0
votes
2
answers
10k
views
Electromagnet Electricity Consumption?
Wikipedia states that -
The only power consumed in a DC electromagnet is due to the resistance of the windings, and is dissipated as heat.
Is this true? So powerful magnets like junkyard magnets ...
- 251
2
votes
1
answer
3k
views
Derive probability current density - factors of 2 discrepancy [closed]
To derive the probability current density for a particle
in an electromagnetic field, we calculate
$\dfrac{\partial \rho}{\partial t}
=
\dfrac{\partial}{\partial t} (\Psi^* \Psi)
=
\dfrac{\partial \...
- 307
0
votes
0
answers
219
views
Are Landau levels always degenerate?
Solving the Landau problem, namely the quantum mechanical problem of a particle in a magnetic field leads to degenerate energy states, the famous Landau levels. My question consists of two parts.
...
- 437
3
votes
1
answer
583
views
Obtaining quantum Hamiltonian for charged particle from path integral formulation
I was working on Shankar 8.6.4, which is about obtaining in one dimension the Hamiltonian operator of a charged particle from the path integral formulation.
First, I get the propagator over a time ...
- 557
2
votes
0
answers
208
views
Second-order correction in Quantum-Confined Stark effect
In the wikipedia article, there is a second-order correction in the Quantum-Confined Stark Effect. I could not understand how it was solved. I did not understand the meaning of 2(0) and 1(0) and how I ...
- 47
2
votes
2
answers
99
views
Transition from 4-potential to E and B [closed]
In my lecture notes there is a step that i cannot follow:
$$\frac{i}{2}[\gamma^{\mu},\gamma^{\nu}] (\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu})=: \sigma^{\mu\nu}F_{\mu\nu}=i\vec{\alpha} \vec{E}-\...
- 139
0
votes
1
answer
309
views
Applying Schrodinger equation to find the energies of a free electron model in a metal [closed]
The one-particle Hamiltonian is given by
$$\hat{H}=\frac{1}{2m}\left(p+\frac{e}{c}A\right)$$
with $e > 0$ and vector potential $A=(0,x,0)B$, such $B=\triangledown \times A=(0,0,B)$
Question:
"I ...
0
votes
2
answers
297
views
How do I properly calculate the curl of the Aharonov-Bohm flux line vector potential?
Given a vector potential describing an infinitely thin line of flux,
$$\vec{A} = \frac{\Phi}{2\pi r} \vec{e}_\varphi,$$
How can I calculate the curl so that the magnetic field is given by
$$\vec{B} ...
- 1,445
0
votes
1
answer
997
views
How do you calculate the free space wavelength of an electron? [closed]
The only thing I know about an electron is that its mass is $m_0 = 9.109 * 10^{-31} kg.$
How would you calculate the wave length from here?
Ok, using de Broglie's relation we have
$p = h/\lambda_e$ ...
- 320
1
vote
2
answers
558
views
Using the force law to obtain total energy of an electron as a function of its radius
I am working on a problem which starts saying determine the total energy of a hydrogen atom with an electron moving with momentum $p$ at a radius $r$.
For that part I got:
$E = \frac{p^2}{2m_e} - \...
- 442
8
votes
1
answer
406
views
Quantum Cyclotron Frequency - Why is it off by a factor of 2?
Say you have a magnetic field $\vec{B}=(0,0,B_0)$. Then the Schrodinger Equation Hamiltonian for a spin-2 particle of charge $e$ moving in this field is:
$$H = \frac{1}{2m}[\vec{p}-e\vec{A}]^2-\vec{\...
- 1,212
5
votes
1
answer
598
views
Aharonov-Bohm Effect in Torus
I had a very brief introduction to the Aharonov-Bohm effect in class. The lecturer introduced the notion that $H(\Phi=\Phi_0)$ and $H(\Phi=0)$ gives identical energy spectrum and that the Hamiltonians ...
- 87
8
votes
1
answer
5k
views
The gauge-invariance of the probability current
It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\
\phi\to\phi-\frac{\partial \chi}{\partial t}\\
\psi\to \psi \exp\left(\frac{iq\chi}{\hbar}\right)\...
- 81