Finite square well potential numerical solution

[Braggplane]

hi guys i need some help with the iteration made in a numerical solution for the eigenstates in a finite square well potential using the effective length approximation

First, i find the eigenstate for a infinite square well, then i define the related alpha and i use it to define an effective length as the nominal one plus 2/alpha, and so on.

the n iteration will use the nominal length plus 2/alpha(n-1) to find the n eigenstate and to define the n alpha (which depends on E)

In this way my equations converge when En=En-1 (and i find the rigth eigenstates).

I have a conceptual doubt: when i define the new length, is the iteration trying to fit the old solution in a new well? (nominal length plus 2/alpha contain almost all the wave function)

but why if i make the same thing with 4/alpha doesn't work?

 

[Quantum Defect]

hi guys i need some help with the iteration made in a numerical solution for the eigenstates in a finite square well potential using the effective length approximation

First, i find the eigenstate for a infinite square well, then i define the related alpha and i use it to define an effective length as the nominal one plus 2/alpha, and so on.

the n iteration will use the nominal length plus 2/alpha(n-1) to find the n eigenstate and to define the n alpha (which depends on E)

In this way my equations converge when En=En-1 (and i find the rigth eigenstates).

I have a conceptual doubt: when i define the new length, is the iteration trying to fit the old solution in a new well? (nominal length plus 2/alpha contain almost all the wave function)

but why if i make the same thing with 4/alpha doesn't work?

I think that we need to see a bit more explained. I am familiar with some methods (Cooley-Numerov) of numerically solving the 1-D Schrödinger equation.

What are you calculating as you iterate? What are you converging to?