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Activities

Computational Activity

120 min.

##### Kinetic energy
Students implement a finite-difference approximation for the kinetic energy operator as a matrix, and then use numpy to solve for eigenvalues and eigenstates, which they visualize.
• Found in: Computational Physics Lab II course(s) Found in: Computational wave function inner products sequence(s)

Small Group Activity

30 min.

##### Operators & Functions
• 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.
• Found in: Quantum Fundamentals course(s)

Small Group Activity

30 min.

##### Superposition States for a Particle on a Ring
Students calculate probabilities for a particle on a ring whose wavefunction is not easily separated into eigenstates by inspection. To find the energy, angular momentum, and position probabilities, students perform integrations with the wavefunction or decompose the wavefunction into a superposition of eigenfunctions.
• Found in: Quantum Ring Sequence sequence(s)

Computational Activity

120 min.

##### Position operator
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.
• Found in: Computational Physics Lab II course(s) Found in: Computational wave function inner products sequence(s)