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.
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.
- How to translate a complicated wavefunction into eigenstates.
- Refresher on how to find expectation values and probabilities in a region.
- How to use the symmetry of the wavefunction to tell you something about measurements.
The Gaussian \begin{equation} {\cal P}(x)=\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-x_0)^2}{2\sigma^2}} \end{equation} is normalized so that the area under the curve is equal to one. If this Gaussian represents the probability density for a free quantum mechanical particle, what is a possible wavefunction?