Help with simple numerical ODE problem from QM

In summary, the conversation is about a numerical analysis problem involving Schrodinger's equation for a one-dimensional trapping potential. The equation given is f''(x) - (x^2 - E_n) * f(x) = 0, and the goal is to find the first five eigenvalues and eigenvectors using a shooting method. The problem is complicated by the lack of given boundary conditions, but it is mentioned that the conditions should be y(-4)= y(4)= 0.
  • #1
mistergrinch
44
0
Here's a simple numerical analysis problem that is confusing me. Can someone help me understand what boundary conditions to use here?

f''(x) - (x^2 - E_n) * f(x) = 0;

Assume f -> 0 as x -> +- inf. This equation comes from Schrodinger's equation for a one dimensional trapping potential, with E_n proportional to energy.

I am supposed to find the first five eigenvalues and eigenvectors with a shooting method, using x in [-4,4], and normalizing f so that int(f^2) = 1;

I'm not given any boundary conditions, so I'm not sure how to solve this problem. Can anyone help me understand what is going on here? Thanks!
 
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  • #2
If you are asked to find eigenvalues, then your boudary conditions have to be y(-4)= y(4)= 0.
 

1. What is a numerical ODE problem?

A numerical ODE problem is a mathematical problem that involves solving an ordinary differential equation (ODE) using numerical methods. This is often necessary when the ODE cannot be solved analytically, or when a precise numerical solution is required.

2. How does this problem relate to quantum mechanics?

This specific problem may involve finding the solution to an ODE that arises in the context of quantum mechanics, such as the Schrödinger equation. The methods used to solve the ODE in this case may be specific to quantum mechanics or may have broader applications.

3. What are some common numerical methods for solving ODEs?

Some common numerical methods for solving ODEs include Euler's method, Runge-Kutta methods, and multistep methods. These methods involve breaking down the ODE into smaller, simpler problems and using iterative calculations to approximate the solution.

4. Do I need any specific programming skills to solve this problem?

While having programming skills may be helpful, it is not necessary to solve a simple numerical ODE problem from quantum mechanics. Many ODE solvers are available as software packages or built into programming languages, so familiarity with coding may be useful but not required.

5. Are there any resources available to help with solving this type of problem?

Yes, there are many resources available for help with solving numerical ODE problems in quantum mechanics. These include textbooks, online tutorials, and forums where you can ask for assistance from experts or other students. It may also be helpful to consult with a professor or TA for guidance.

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