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.
 Write each of eleven given states in bra/ket notation.

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.

Which of the 11 states are are rightmoving? Generalize your result to give a characterization of the set of all possible states that are rightmoving.

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.

Compare the time dependence of the three states: \(\left{\Psi_{T3}}\right\rangle , \left{\Psi_{T4}}\right\rangle , \left{\Psi_{T5}}\right\rangle \)