keyboard Computational Activity

120 min.

Position operator

Computational Physics Lab II 2022

quantum mechanics operator matrix element particle in a box eigenfunction

Students find matrix elements of the position operator \(\hat x\) in a sinusoidal basis. This allows them to express this operator as a matrix, which they can then numerically diagonalize and visualize the eigenfunctions.

group Small Group Activity

30 min.

Wavefunctions on a Quantum Ring

Central Forces 2023 (2 years)

group Small Group Activity

30 min.

Operators & Functions

Quantum Fundamentals 2023 (3 years) Students are asked to:

• Test to see if one of the given functions is an eigenfunction of the given operator
• See if they can write the functions that are found not to be eigenfunctions as a linear combination of eigenfunctions.

group Small Group Activity

30 min.

Quantum Expectation Values

Quantum Fundamentals 2023 (3 years)

keyboard Computational Activity

120 min.

Sinusoidal basis set

Computational Physics Lab II 2023 (2 years)

inner product wave function quantum mechanics particle in a box

Students compute inner products to expand a wave function in a sinusoidal basis set. This activity introduces the inner product for wave functions, and the idea of approximating a wave function using a finite set of basis functions.