Solving schrodingers numerically

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SUMMARY

This discussion focuses on numerically solving the time-independent Schrödinger equation, specifically for the potential V(X) = X^2. The user successfully implements a modified Runge-Kutta method to find even solutions with initial conditions Y(0) = 1 and Y'(0) = 0. However, they encounter difficulties adapting their program to find odd solutions, initially attempting Y(0) = 0 and Y'(0) = 1, which did not yield the desired results. The user also inquires about the eigenvalues of even and odd solutions when the potential is set to V(X) = -1/(1 + X^4).

PREREQUISITES
  • Understanding of the Schrödinger equation and its applications in quantum mechanics
  • Familiarity with numerical methods, specifically the modified Runge-Kutta method
  • Knowledge of boundary value problems and initial conditions in differential equations
  • Basic concepts of eigenvalues and eigenfunctions in quantum systems
NEXT STEPS
  • Research the implementation of the modified Runge-Kutta method for solving differential equations
  • Explore techniques for solving boundary value problems in quantum mechanics
  • Learn about eigenvalue problems in quantum systems, particularly for different potentials
  • Investigate numerical methods for solving the Schrödinger equation with complex potentials
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Quantum physicists, computational scientists, and students studying numerical methods in quantum mechanics will benefit from this discussion.

Nigel_baxter
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hi guys. this is my first post so hello to everyone here!
right, well to my problem. I'm attempting to solve (numerically) schrodingers equation.
ie time independent one, which can be taken as (d/dX2 + V(X))Y(X)=E*Y(X) (after defining a dimensionless constant to get rid of all the "junk" ;) )
first i am given that the potential V(X)=X*X and that the initial conditions that Y(0)=1 and Y'(0)=0, which is "appropriate for an even solution".
I then solve it numerically quite easily using a modified rungekutta method.
However i am not use how to adapt my program in order to solve for an odd solution...would it simply be a change of initial conditions?

thank you for the help guys, it is well appreciated.
 
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Try Y(0)=0 and Y'(0)=1 ?
 
yes i did try that, but it does not give me the answer i want.
i forgot to mention, i only need to get the even and odd solutions when the potential is (-1/(1+x^4)).
also when i do find even and odd solutions, should they share the same eigenvalues?
thank you again
 

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