## Particle on a Ring Time Dependence: Mathematica Notebook

• Central Forces 2021

(2 points each)

Answer the following questions for a quantum mechanical particle confined to a ring. Use the Mathematica worksheet (cfqmring.nb) on time dependence on the ring to help you figure out the answers.

1. Write each of eleven given states in bra/ket notation.
2. For which of the 11 states does the probability density not depend on time? These are called stationary states. Generalize your result to give a characterization of the set of all possible states that are stationary states.
3. Which of the 11 states are are right-moving? Generalize your result to give a characterization of the set of all possible states that are right-moving.
4. Which of the 11 states form standing waves? Generalize your result to give a characterization of the set of all possible states that are standing waves.
5. Compare the time dependence of the three states: $\left|{\Psi_{T3}}\right\rangle , \left|{\Psi_{T4}}\right\rangle , \left|{\Psi_{T5}}\right\rangle$