Initial condition of Wave functions with Yukawa Potential

Riccardo Marinelli
Homework Statement:
Find eigenfunctions of Schrödinger equation with Yukawa potential
Relevant Equations:
$$V(r)=-\frac{1}{r}\exp{-\frac{r}{r_0}}$$
Hello, I was going to solve with a calculator the eigenvalues problem of the Schrödinger equation with Yukawa potential and I was thinking that the boundary conditions on the eigenfunctions could be the same as in the case of Coulomb potential because for r -> 0 the exponential term goes to 1, am I right or have I to be more careful?
In the case I'm wrong do you know some articles or books where I can find some information about these conditions?

Last edited:

Gold Member
correct and the wave function needs to go to $0$ as $r \rightarrow \infty$

Riccardo Marinelli
Yes, in order to find the eigenvalue I impose that the wavefunction goes to zero, thank you

Homework Helper
Gold Member
2022 Award
Homework Statement:: Find eigenfunctions of Schrödinger equation with Yukawa potential
Relevant Equations:: $V(r)=-\frac{1}{r}\exp{-\frac{r}{r_0}}$

Hello, I was going to solve with a calculator the eigenvalues problem of the Schrödinger equation with Yukawa potential and I was thinking that the boundary conditions on the eigenfunctions could be the same as in the case of Coulomb potential because for r -> 0 the exponential term goes to 1, am I right or have I to be more careful?
In the case I'm wrong do you know some articles or books where I can find some information about these conditions?

You're a couple of dollars short there:
$$V(r)=-\frac{1}{r}\exp{-\frac{r}{r_0}}$$

TSny and Riccardo Marinelli
Riccardo Marinelli
Thank You ! I was wondering how to insert Latex properly!