Activities
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.
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 \(L_z\).
Students use a PhET simulation to explore the time evolution of a particle in an infinite square well potential.
In this lecture, the instructor guides a discussion about translating between bra-ket notation and wavefunction notation for quantum systems.
Students find a wavefunction that corresponds to a Gaussian probability density.
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:
- normalize the wave function,
- find the probability that the particle is measured to be in the range \(0<x<1\).