**Transcription:**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?

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