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Activities

Small Group Activity

60 min.

Going from Spin States to Wavefunctions
Students review using the Arms representation to represent states for discrete quantum systems and connecting the Arms representation to histogram and matrix representation. The student then extend the Arms representation to begin exploring the continuous position basis.

Small Group Activity

30 min.

Wavefunctions on a Quantum Ring
This activity lets students explore translating a wavefunction that isn't obviously made up of eigenstates at first glance into ket and matrix form. Then students explore wave functions, probabilities in a region, expectation values, and what wavefunctions can tell you about measurements of \(L_z\).
In this lecture, the instructor guides a discussion about translating between bra-ket notation and wavefunction notation for quantum systems.

Small White Board Question

5 min.

Normalization of the Gaussian for Wavefunctions
Students find a wavefunction that corresponds to a Gaussian probability density.
  • Found in: Periodic Systems course(s) Found in: Fourier Transforms and Wave Packets sequence(s)

Problem

5 min.

Wavefunctions

Consider the following wave functions (over all space - not the infinite square well!):

\(\psi_a(x) = A e^{-x^2/3}\)

\(\psi_b(x) = B \frac{1}{x^2+2} \)

\(\psi_c(x) = C \;\mbox{sech}\left(\frac{x}{5}\right)\) (“sech” is the hyperbolic secant function.)

In each case:

  1. normalize the wave function,
  2. find the probability that the particle is measured to be in the range \(0<x<1\).

  • Found in: Quantum Fundamentals course(s)