Solving schrodingers numerically

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In summary, The conversation discusses the speaker's attempt to numerically solve the time independent Schrodinger's equation using a modified Runge-Kutta method. The initial conditions and potential are given, and the speaker is able to solve for an even solution but is unsure how to adapt the program for an odd solution. Suggestions are made to change the initial conditions to Y(0)=0 and Y'(0)=1, but the speaker states that this does not give the desired answer. The speaker also mentions that they only need to find even and odd solutions for a specific potential and asks if they should have the same eigenvalues. The speaker expresses gratitude for the help received.
  • #1
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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  • #2
Try Y(0)=0 and Y'(0)=1 ?
 
  • #3
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
 

1. How is Schrödinger's equation solved numerically?

Schrödinger's equation is solved numerically using a variety of methods, such as the finite difference method, finite element method, and variational method. These methods involve discretizing the equation into smaller parts and using numerical techniques to solve for the wave function at each point.

2. What is the significance of solving Schrödinger's equation numerically?

Solving Schrödinger's equation numerically allows us to study quantum mechanical systems and predict their behavior, such as the energy levels and wave functions of particles. It also allows us to model complex systems that cannot be solved analytically.

3. What are some challenges in solving Schrödinger's equation numerically?

Some challenges in solving Schrödinger's equation numerically include accurately representing the potential energy function, dealing with complex boundary conditions, and ensuring numerical stability and convergence.

4. Can Schrödinger's equation be solved analytically?

Yes, Schrödinger's equation can be solved analytically for simple systems with well-defined potentials. However, for more complex systems, it is often necessary to use numerical methods to obtain solutions.

5. How does solving Schrödinger's equation numerically compare to other methods?

Solving Schrödinger's equation numerically is often more computationally intensive compared to other methods, such as perturbation theory or the variational method. It also requires a good understanding of numerical techniques and their limitations. However, it allows us to study a wider range of systems and provides more accurate results in many cases.

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