Initial condition of Wave functions with Yukawa Potential

  • #1
Riccardo Marinelli
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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?
 
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Answers and Replies

  • #2
Dr Transport
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correct and the wave function needs to go to [itex] 0 [/itex] as [itex] r \rightarrow \infty [/itex]
 
  • #3
Riccardo Marinelli
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Yes, in order to find the eigenvalue I impose that the wavefunction goes to zero, thank you
 
  • #4
PeroK
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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:
$$V(r)=-\frac{1}{r}\exp{-\frac{r}{r_0}}$$
 
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  • #5
Riccardo Marinelli
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Thank You ! I was wondering how to insert Latex properly!
 

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