All Questions
15
questions
0
votes
1
answer
440
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
1
vote
0
answers
187
views
Potential energy and atomic units in the Bohr model
I have a question regarding the final sentence written in the solution to part iii) (found below) for the question given below.
In the Bohr model of the hydrogen atom, the radius of the electron ...
- 156
2
votes
1
answer
156
views
Intuiting qualitatively the shapes of the eigenfunctions of a finite well-like potential, using the infinite well eigenfunctions as an inspiration
Consider, for example, the third excited state of an infinite square well:
Now consider the following potential:
If we wanted to sketch the rough shape of the third excited eigenfunction of this ...
- 1,307
4
votes
2
answers
338
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
2
answers
783
views
Classical period of Morse potential [closed]
A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential:
$$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$
From the only other question I have ...
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
3
votes
2
answers
1k
views
Perturbation theory with infinite potential
I'm trying to solve an excercise that involves first order perturbation theory and an infinite potential. To ease the problem, I tried to consider an easier one dimensional model. Consider an infinite ...
- 93
1
vote
1
answer
184
views
The energy difference between $H$ atom and $H^+$ ion in Thomas Fermi Theory
The famous Thomas Fermi theory says that we can express the total energy of a atomic system with $N$ electrons orbiting around a charged nucleus of atomic number $Z$ in terms of radial density of ...
1
vote
1
answer
1k
views
Well-defined momentum
I have a question which states:
Show that a particle can have a well-defined momentum in every energy eigenstate if and only if the potential energy is uniform in space.
I am completely unsure how ...
- 77
3
votes
4
answers
2k
views
Meaning of transmission coefficient greater than one in a potential well problem
Consider the finite 1D wedge-shaped potential well given by
$$V(x)=V_0\left(\frac{|x|}{a}-1\right) \hspace{10pt}\mathrm{for}\hspace{3pt} |x|<a;\hspace{6pt}V(x)=0 \hspace{10pt}\mathrm{for}\hspace{...
- 912
0
votes
2
answers
3k
views
Particle in a finite well: Potential energy function
I'm a chemist, not a physicist, but am taking a quantum chemistry course right now and I'm having difficulty grappling with the following:
For the particle in a finite potential well, so long as no ...
- 687
1
vote
1
answer
766
views
De Broglie wave length of electron [closed]
Consider an electron with total energy $E>V_2$ in a potential well with
$$V(x)= \begin{cases}
\infty & x< 0 \\
V_1 & 0< x< L \\
V_2 & x>L
\end{cases}
...
- 568
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 ...
user100411
4
votes
1
answer
6k
views
Derivation of Interaction energy of Dipole - Induced Dipole Interaction
I see that the formula giving the potential (interaction) energy of a dipole and an induced dipole is $$V=-\frac{C}{r^6}$$ where $$C=\frac{\mu_1^2 \alpha'_2}{4 \pi \epsilon_0}$$ and that the formula ...
- 345