Linked Questions

1
vote
0answers
81 views

How can theories about 1D or 2D systems be generalized for 3D systems?

I was watching a lecture video from MITx $^\dagger$ by professor Barton Zwiebach. He proved a pretty cool theorem "every attractive 1-dimensional potential has a bound state"; however, that only holds ...
0
votes
1answer
253 views

Question on Uncertainty Principle in a Potential Well

The following is the problem that I'm struggling with from the book of Gasiorowicz: If we have an electron in a potential well of width $a$ and depth $V_0$, then the kinetic energy is, by the ...
4
votes
5answers
2k views

Why does a delta-function well have only 1 bound state?

From Griffiths, Introduction to Quantum Mechanics, pg. 73: Evidently, the delta-function well, regardless of its "strength" $\alpha$, has exactly one bound state $$\psi(x) = \frac{\sqrt{m \...
2
votes
2answers
1k views

How to predict bound states in a 1D triangular well?

Assume we have a (single) particle in a potential well of the following shape: For $x \leq 0$, $V = \infty$ (Region I) For $x \geq L$, $V = 0$ (Region III) For the interval $x > 0$ to $x < L$,...
0
votes
1answer
134 views

Bound state in potential less 0

How to prove that there is a bound state in the potential $U(x) = -A e^{-a |x|}$, where for all $a \in \mathbb{R}$ and $A>0$. I heard that we can say something to the minimum of this form $ \left( \...
13
votes
3answers
1k views

Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential?

The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they? If yes, can we look for ...
4
votes
0answers
163 views

Bound states in 1D & 2D [duplicate]

Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D? See, for example, this article, arXiv:math-ph/0208011.
0
votes
0answers
231 views

How to compute minimum shallowness of quantum well to have at least one bound state?

Given a potential $V$, how does one compute how shallow the potential can be such that it allows at least one bound state?
7
votes
1answer
1k views

Am I missing a trick to solving a 3D potential well problem?

I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0>0$ otherwise. By using the Schrödinger Equation, I showed that: $$\frac{-\hbar}{2m}\frac{1}{r^...
-1
votes
1answer
306 views

Quantum mechanics: Finite square well problem

What will happen if the potential is less than 0, for instance $V(x)=-10eV$. Is this means there will be no bound states? Since solution to the time independent Schrodinger equation (those discrete ...