Example Proposal: Quantum Tunneling¶

Project Goal:¶

Modeling the probability of a particle quantum tunneling through a finite barrier

Plan to achieve goal:¶

Can combine FDMs and Schrodinger's equation, similar to Laplace equation problem
Needed to set up boundaries, describe specific setup of the problem
Need to set up a matrix equation and solve for the solution
Model the probability, which can be calculated from wavefunction (this is what we will be solving for)

Loosely defined coding plan:¶

set up numpy array to track wavefunction values (with x and t dimensions)
put boundary conditions into the above array (including starting wavefunction as a delta function)
set up other variables for other stuff in Schrodinger's equation (including the finite potential barrier)
write out system of equations (this is the only part that's not code)
set up numpy arrays for matrix equation: if N unknowns, then an N x N matrix, and a N x 1 vector
place each equation into the matrix and the vector, using loops to take advantage of the fact that system of equations all probably have similar structure. Indexing could be tricky here!
solve matrix problem using linalg.solve
by then we should have all wavefunction values, which can be used to compute probabilities and reach the solution!

List of major computing tools/concepts that each group member could focus on individually:¶

numpy arrays
- will be used throughout
loops
- will be used to populate matrices
finite difference methods
- will be used to set up system of equations
systems of equations/matrices
- will be used to solve!
if statements
- will be used to populate matrices
visualization
- will be used to demonstrate solution in a presentable manner

Plan of work:¶

(There is not an example for this. But you are expected to include this in your proposal! Each team should come up with a personalized plan that suits the members of that team)

This is where you describe how the team will participate together, communicate, handle potential conflict, and ultimately complete the project
If you are working individually, you should address your own plan for how/when you will work on this and ensure you are making the progress you need to make