A free particle of mass m lives on a circle of length L. The circle can alternately be thought of as a line segment from x=0 to x-L with periodic boundary conditions, that is, any function f(x) must satisfy f(0)=f(L). a. Write the Schrodinger equation. Hint: By "free particle" we mean that the potential vanishes. b. Solve the Schrodinger equation. c. Normalize the wavefunctions. d. What are the energy eigenvalues?

A free particle of mass m lives on a circle of length L. The circle can alternately be thought of as a line segment from x=0 to x-L with periodic boundary conditions, that is, any function f(x) must satisfy f(0)=f(L). a. Write the Schrodinger equation. Hint: By "free particle" we mean that the potential vanishes. b. Solve the Schrodinger equation. c. Normalize the wavefunctions. d. What are the energy eigenvalues?