QM Ring Time

• Central Forces 2021

  Answer the following questions for a quantum mechanical particle confined to a ring. You may want to use the Mathematica Notebook or the GeoGebra applet on time dependence on the ring to help you figure out the answers.

  1. Characterize the states for which the probability density does not depend on time. States for which the probability density does not depend on time are called stationary states.
  2. Characterize the states that are right-moving.
  3. Characterize the states that are standing waves.

  4. Compare the time dependence of the three states: \begin{align} \vert \Psi_1\rangle &= \frac{1}{\sqrt{2}}\left(\vert 2\rangle + \vert -2 \rangle\right)\\ \vert \Psi_2\rangle &= \frac{1}{\sqrt{2}}\left(\vert 2\rangle - \vert -2 \rangle\right)\\ \vert \Psi_3\rangle &= \frac{1}{\sqrt{2}}\left(\vert 2\rangle + i \vert -2 \rangle\right) \end{align}