All Questions
Tagged with scattering schroedinger-equation
157
questions
2
votes
2
answers
87
views
Question on 1D Scattering Resonances
I'm reading Henley and Garcia's Subatomic Physics. To introduce the concept of resonances they use a 1D square well scattering example. Resonances are where the transmission coefficient goes to one.
...
- 2,540
0
votes
1
answer
146
views
Green function in scattering theory
I'm having a bit of trouble with a step in scattering theory.
Context:
The Schrödinger equation for a two-body scattering problem can be written as:
$$
(E - H_0) |\psi\rangle = V |\psi\rangle.
$$
Here,...
- 319
0
votes
1
answer
41
views
Reflection of quantum particle colliding with a potential barrier
Let a quantum particle be subject to a one dimensional step potential barrier $V$ such that:
$$V(x)=\begin{cases}0, \ x<0 \\ V_0, \ x>0\end{cases}$$
where the particle's energy is $E>V_0>0$...
- 1,616
1
vote
2
answers
43
views
Are reflection and transmission coefficients in 1D problem are independent of the direction in which we choose as incident?
I was watching a lecture series of Quantum mechanics of Professor V. Balakrishnan,
There was a problem session,
“For an arbitrary potential barrier (any potential function of position and it need not ...
0
votes
1
answer
122
views
Scattering Matrix and the Lippmann-Schwinger equation in QM
I am currently studying scattering theory from the Sakurai's quantum mechanics. I have previously studied this subject from Griffith's quantum mechanics. In the latter textbook, scattering matrices ...
- 199
1
vote
1
answer
75
views
Difference between stationary states, collision states, scattering states, and bound states
A few weeks ago, I was presented one-dimensional systems in my QM class, and of course one-dimensional potentials too. Nonetheless, I'm still a bit unclear about the terminology my professor uses. ...
- 1,616
0
votes
2
answers
63
views
Justification of discarding the backward wave in step potential scattering
I'm following Shankar's treatment of 1D scattering in Principles of Quantum Mechanics (Page 167 to Page 172).
In general, the eigenstates of the single-step potential $$V(x)=\begin{cases}
0 & \...
- 35
0
votes
1
answer
54
views
Boundary condition of hard wall potential
I have a potential that is like
$$
V(x)= \left\{\begin{matrix}
0 & x >0 \\
\infty & x \leq 0 \\
\end{matrix}\right.
$$
Using the boundary condition at $\psi(x=0)=0$ I have found that the ...
0
votes
1
answer
114
views
Born approximation for 1D scattering using Green's function
For $1D$ scattering, we can write a recursive equation for the wave function:
$$\psi(x) = Ae^{ikx} + \int dx'\frac{e^{ik|(x-x')|}}{2ik}\frac{2m}{\hbar^2}V(x')\psi(x')$$
I am trying to show that ...
- 351
0
votes
0
answers
37
views
Reflections from both edges of a finite well
In section 11.3.1 in Richard Robinnett's Quantum Mechanics book, it says that in the case of transmission resonance ($T=1$), there's complete destructive interference between waves reflected from the ...
- 860
0
votes
1
answer
74
views
Interpretation of zero energy Schrödinger equation
Consider two identical bosons with Hamiltonian given by:
$$H_{2} = -\nabla_{x_{1}}^{2}-\nabla_{x_{2}}^{2}+V(x-y)$$
acting on the subspace of symmetric functions on $L^{2}(\mathbb{R}^{3})$. Here, $V$ ...
- 1,131
1
vote
0
answers
57
views
The derivative of the wave function at the boundary of the wall with potential $U_0$ ($m_1 \neq m_2$) [closed]
In the potential barrier, if a particle in an environment with a potential of $U_1$ hits a potential barrier with $U_2$ and suppose its energy is less than $U_2$.
Now my question is that if the mass ...
- 111
0
votes
1
answer
75
views
Step Potential versus Free particle [duplicate]
In the step potential
\begin{equation}
V=
\begin{cases}
0 &, \text{x<0}\\
V_0 &, \text{x>0}
\end{cases}
\end{equation}
for the scattering states$(E>V_0)$, the states on the right and ...
- 860
5
votes
1
answer
244
views
Details in the derivation of the Lippmann-Schwinger equation
So the argument goes that for a slightly perturbed Hamiltonian
$$
H = H_0 + V,
$$
there will be some exactly known states, $\left|\phi\right>$, solving
$$
H_0\left|\phi\right> = E\left|\phi\...
- 525
1
vote
0
answers
76
views
Boundary conditions required to get a unique solution to Schrodinger Equation
If we are considering the scattering of an electron plane wave from a crystal specimen, we could start with the time-independent Schrodinger equation (TISE) as our governing equation:
$$ \{\nabla^2 + ...
- 83