Finite difference method for even potential in QM

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SUMMARY

The discussion focuses on the application of the Finite Difference (FD) method for solving quantum mechanics problems involving even potential, specifically in the context of a homework assignment related to Nanotechnology and Nanocomponents. The user encounters difficulties with boundary conditions when applying the FD method only in the x>0 domain, contrasting with previous experiences where the wave function vanishes at the endpoints. The user seeks guidance on the necessary steps to resolve these boundary condition issues effectively.

PREREQUISITES
  • Understanding of the Finite Difference method in numerical analysis
  • Familiarity with quantum mechanics concepts, particularly wave functions
  • Knowledge of boundary conditions in differential equations
  • Basic skills in mathematical modeling and problem-solving in physics
NEXT STEPS
  • Research the application of boundary conditions in the Finite Difference method
  • Study the implications of even potential in quantum mechanics
  • Learn about numerical stability and convergence in FD methods
  • Explore advanced topics in quantum mechanics related to potential wells and barriers
USEFUL FOR

Students and researchers in physics, particularly those studying quantum mechanics and numerical methods, as well as educators teaching courses in Nanotechnology and Nanocomponents.

Nemanja989
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Hello to everyone,

while solving homework course Nanotechnology and Nanocomponents, I have encountered a problem in FD method that is applied in even potential. In my homework assignment it is explicitly said that it must be done only in x>0 part of the domain, where my problem starts with boundary conditions. Previously we have worked FD method in class but in general case, and we used conditions that wave function vanishes at the end points. The rest of the problem I have wrote and attached to this message as a pdf.
 

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I would be grateful if somebody could help me out with this problem and explain the steps that should be taken in order to solve it.Thank you very much in advance.
 

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