A particle of mass m moves in a dimension between -L/2 and L/2. Within these limits the potential V=0. At distances greater than L/2 and less than -L/2 the potential V is infinite. This is a particle in the distance box L, between -L/2 and +L/2. By solving the Schrdinger equation for this system it established that the wave function for this system can be expressed as (x)=Ncos(kx). After normalizing the function is (x)=1/L cos ((2n+1)/L)x.

a. State the energy expression for this system. (Hint: You must state, not solve, the differential equation of this system where the relationship of k to energy is found.)

b. State, do not solve, the expectation values and

for this system.