All Questions
7
questions
0
votes
1
answer
85
views
Schrödinger-Propagator for combined linear and harmonic potential
Given the Hamiltonian
\begin{equation}
H = \frac{p^2}{2m} + V(x)
\end{equation}
The propagator for a pure harmonic potential of the form
\begin{equation}
V(x) = \frac{1}{2} m \omega^2 x^2
\end{...
- 141
0
votes
1
answer
434
views
Finite potential well and nature of its solutions
The question I have is about nature of solutions, not a solution or a specific answer that I am looking for. If we define a potential well centred at $x=0$ as the following,
$$V(x) = \left\{ \begin{...
- 131
2
votes
2
answers
1k
views
Why can't energy be below the minimum of the potential in a bound state? [duplicate]
I just stumbled across the problem and have no idea how to solve it:
"Considering the Time-Independent Schrodinger Equation for a stationary state $\psi$ with energy $E$, that is $$\psi '' = \...
- 418
4
votes
2
answers
337
views
How to solve Schroedinger's equation with Kratzer potential?
Kratzer potential is defined by
$$V(r)={\frac{\alpha}{r}+\frac{\beta}{r^2}}.$$
I read that the Schroedinger equation for this potential has an analytical solution in terms of hypergeometric ...
- 1,088
0
votes
1
answer
1k
views
Finite square well bound states
Let's suppose I have a finite potential well: $$
V(x)=
\begin{cases}
\infty,\quad x<0\\
0,\quad 0<x<a\\
V_o,\quad x>a.
\end{cases}
$$
I solved the time-independent Schrodinger equation ...
- 113
0
votes
2
answers
3k
views
Particle in a finite well: Potential energy function
I'm a chemist, not a physicist, but am taking a quantum chemistry course right now and I'm having difficulty grappling with the following:
For the particle in a finite potential well, so long as no ...
- 687
1
vote
2
answers
3k
views
Wave function for step potential
Given the step potential
$$V(x)=\begin{cases}
0~~~~~~~~\text{if }~~x \leq 0 \\
V_0~~~~~~\text{if }~~x > 0
\end{cases}$$
Consider the case where $E < V_0$. In this region $x \leq 0$ we have ...
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