Delta well + infinite barrier -> bound state

Click For Summary
The discussion focuses on the quantum mechanical analysis of a potential defined by an infinite barrier and a delta function well, specifically examining the conditions for bound states. The participants explore the wavefunction forms in different regions and derive relationships involving the parameters λ and d for the existence of bound states. A key finding is that the condition for at least one bound state is given by the inequality 2mλd/ħ² > 1, indicating a dependence on both the strength of the delta potential and its position. The conversation also touches on the nature of bound states, emphasizing that solutions must be normalizable and decay exponentially in the appropriate region. Ultimately, the discussion clarifies the complexities of defining bound states in the context of this specific potential.
  • #31
reilly said:
Think of the delta function, with positive lambda, as a very narrow, deep potential well. Use your common sense and experience with the potential well to get the appropriate general form of the solution.
Regards,
Reilly Atkinson

Reilly, thanks for your reply, but which part are you referring to?

As I stated in an earlier post, I was able to get the bound state solution. But in post #18, I posed the second part of the problem, which deals with the asymptotic nature of the wavefunction in case of a scattering problem for the same V(x). I solved that and got an equation for the phase shift.

But as far as I can tell, the phase shift can be determined exactly from that equation and unless I have made a mistake in the computation, there is no need to assume that \phi \approx ak and determine a as the question demands.
 

Similar threads

A Dimension of \lambda constant in \delta potential
  • · Replies 2 ·
Replies
2
Views
922
I Mathematical basics of quantum mechanics
  • · Replies 21 ·
Replies
21
Views
3K
A Weyl Fermion in an infinite well
  • · Replies 1 ·
Replies
1
Views
1K
A A particle locked inside an arrangement of Dirac delta potentials
  • · Replies 4 ·
Replies
4
Views
1K
I I would like an explanation of these extra energy states
  • · Replies 3 ·
Replies
3
Views
984
A Solving Schrödinger's Equation with a Smooth Potential Wall: A Detailed Guide
  • · Replies 2 ·
Replies
2
Views
1K
I Finite square well bound states
  • · Replies 1 ·
Replies
1
Views
2K
A Ground state calculation with a time averaged wave function
  • · Replies 2 ·
Replies
2
Views
1K
I Solving Schrodinger's eqn using ladder operators for potential V
  • · Replies 4 ·
Replies
4
Views
2K
A Power series in quantum mechanics
  • · Replies 1 ·
Replies
1
Views
1K