Tagged Questions
3
votes
1answer
73 views
Tunneling and transmission
Lets say we have a tunelling problem in the picture, where $W_p$ is a finite potential step:
If particle is comming from the left a general solutions to the Schrödinger equations for sepparate ...
0
votes
1answer
99 views
Potential step and its transmission / reflection
Lets say we have a potential step with regions 1 with zero potential $W_p\!=\!0$ (this is a free particle) and region 2 with potential $W_p$. Wave functions in this case are:
\begin{align}
...
0
votes
0answers
44 views
Wave equations for two intervals at Potential step
Lets say we have a potential step as in the picture:
In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$.
Let me ...
0
votes
0answers
92 views
Scattering and partial wave analysis for cross section [closed]
Problem
Given the central potential:
$V(r)=-\frac{\hbar^2}{m a^2}\frac{1}{\cosh({r\over a})}$
and given that we know the solution to the following ODE
$\frac{d^2 y}{dx^2}+k^2 ...
2
votes
1answer
56 views
In the expansion of the scattered wave function, why do these two functions have the same index?
See Griffiths Quantum Mechanics, eq. 11.21. Evidently,
$$\psi(r,\theta,\phi)=Ae^{ikz}+A\sum\limits_{l,m}^{\infty}C_{l,m}h_{l}(kr)Y_{l}^{m}(\theta,\phi).$$
But I don't see why the $l$th Hankel function ...
5
votes
3answers
307 views
Particle coming across a step potential barrier
My quantum mechanics textbook says that when a particle (in the classical case) comes across a potential-step barrier of finite height, if it has sufficient energy to surmount the barrier, it will ...
1
vote
1answer
91 views
Scattering from a box potential of width $L$ doesn't reproduce a step potential in the limit $L \rightarrow \infty$
Consider the scattering of a quantum particle in one dimension, caused by a step in the potential (this appears in many undergrad level QM books):
$$ V(x) = \begin{cases} V_1 & x<0 \\ V_2 ...
4
votes
1answer
142 views
Scattering states of Hydrogen atom in non-relativistic perturbation theory
In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states
$$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' ...
1
vote
1answer
430 views
Plane wave expansion in cylindrical coordinates
I am trying to solve scattering problem in 2D and got to expand the wave function in cylindrical system which comes out to be Hankel function. Can you tell me how to expand the plane wave $\exp(i ...
1
vote
1answer
307 views
Electron Incident On A Finite Potential Barrier
This is problem 2.8.3 from Miller's Quantum Mechanics For Scientists And Engineers. I'm getting stuck when I try to figure out the wave equation on the right-hand side of the barrier. The original ...
6
votes
1answer
412 views
Proof of Yang's theorem
Yang's theorem states that a massive spin-1 particle cannot decay into a pair of identical massless spin-1 particles. The proof starts by going to the rest frame of the decaying particle, and relies ...
1
vote
0answers
340 views
Scattering on delta function potential
Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$.
How can one show or explain that ...
1
vote
2answers
290 views
Compton scattering angle
Say a photon hits a free electron at rest. I understand that there is a formula for the Compton scattering when the photon is scattered with an angle $\theta$, but I don't understand what determines ...
1
vote
2answers
156 views
Compton scattering multiple wavelengths?
The formula given for compton scattering shows that when x-ray of one specific wavelength hits carbon or some materials, emitted x-ray will be of one new specific wavelength.
However, according to ...
2
votes
1answer
81 views
When does the “norm of quasi-eigenvectors” matter in calculations? For which physical results are these even used?
Which physical system in nonrelativistic quantum mechanics is actually described by a model, where the norm of the "position eigenstate" (i.e. the delta distribution as limit of vectors in the ...
2
votes
2answers
253 views
At what angle does a single atom “reflect” a single photon?
Does this question make sense in the quantum world?
Imagining a single photon (wave packet?) interacting with a single atom (its electrons etc) how do we currently describe/define the emitted photon ...
5
votes
2answers
908 views
Why are scattering matrices unitary?
In Griffith's QM book, he introduces scattering matrices as an end-of-the-chapter problem.
For a Dirac-Delta potential $V(x) = \alpha \delta (x - x_0)$, I've derived the scattering matrix and ...
2
votes
1answer
86 views
Cross sections and renormalization scheme
Can the result on cross section of some process be dependent on the renormalization scheme used?
0
votes
1answer
247 views
Phase shift for Scattering in radial potentials
given a radial potential in 3 dimension and its Schroedinguer equation
$ -D^{2}U(r) + \frac{l(l+1)}{r^{2}}+V(r) $ here D means derivative with respect to 'r'
then if we apply quantum scattering how ...
3
votes
0answers
319 views
Raman Scattering and the Kramers-Heisenberg Formula
Using the words of the wikipedia article Raman Scattering:
The Raman effect corresponds, in perturbation theory, to the absorption and subsequent emission of a photon via an intermediate ...
14
votes
6answers
950 views
Why can we treat quantum scattering problems as time-independent?
From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this:
Solve the time-independent Schrodinger ...
2
votes
1answer
672 views
What is the Jost function in scattering theory?
What is the Jost function in scattering theory? Is it an operator or some kind of determinant? How is it obtained?
10
votes
1answer
2k views
Phase shifts in scattering theory
I have been studying scattering theory in Sakurai's quantum mechanics. The phase shift in scattering theory has been a major conceptual and computational stumbling block for me.
How (if at all) does ...
8
votes
2answers
498 views
Calculation of the cross section
Why, when we calculate the total cross section, we make the average other initial states and the sum over final states?
3
votes
1answer
633 views
Fermi's Golden Rule
It is well known that to calculate the probability of transition in the scattering processes, as a first approximation, we use the Fermi golden rule. This rule is obtained considering the initial ...
