Boundary conditions of eigenfunctions with Yukawa potential

Click For Summary
SUMMARY

The discussion centers on the boundary conditions of eigenfunctions in the Schrödinger equation with Yukawa potential. It confirms that the boundary conditions at r=0 for the radial wave function are indeed the same as those for the Coulomb potential. Additionally, it emphasizes that at r → ∞, only one boundary condition is necessary for bound states, which results in quantized energy eigenvalues similar to those of the hydrogen atom. The conversation highlights the importance of understanding these boundary conditions for accurate numerical solutions.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with Yukawa potential
  • Knowledge of boundary conditions in quantum mechanics
  • Experience with numerical methods for solving differential equations
NEXT STEPS
  • Research the properties of Yukawa potential in quantum mechanics
  • Study boundary conditions for radial wave functions in quantum systems
  • Explore numerical methods for solving the Schrödinger equation
  • Investigate quantization of energy eigenvalues in bound states
USEFUL FOR

Physicists, quantum mechanics students, and researchers interested in solving eigenvalue problems related to Yukawa potential and understanding boundary conditions in quantum systems.

Riccardo Marinelli
Messages
5
Reaction score
1
TL;DR
Where can I find information about the boundary condition of eigenfunctions of the schrödinger equation with Yukawa potential?
Hello, I was going to solve numerically the eigenfunctions and eigenvalues problem of the schrödinger equation with Yukawa Potential. I thought that the Boundary condition of the eigenfunctions could be the same as in the case of Coulomb potential. Am I wrong? In that case, do you know some articles/books where I can find information about that?
 
Physics news on Phys.org
Which boundary conditions are you referring to? For the radial wave function the ones at ##r=0## should indeed be the same as for the Coulomb potential. For ##r \rightarrow \infty## you only need one for the bound states, which leads to the quantized energy eigenvalues as for the hydrogen atom.
 
Hi, I was referring to the boundary conditions in r=0, thank you for your reply
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 31 ·
2
Replies
31
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 17 ·
Replies
17
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 93 ·
4
Replies
93
Views
6K
  • · Replies 24 ·
Replies
24
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K