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 and it can be established that the wave function for this system can be expressed as (x)=Ncos(kx).

a.Use the boundary conditions and determine the value of k.

b.Normalize this function.

c. For the second energy state of this system, indicate the maximum and minimum values within this one-dimensional box.

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

for this system.