## Problems in quantum mechanics (3)

December 2, 2012 by micropore

A particle of mass *m* is confined to a one-dimensional region *0≤x≤a*. At the beginning, the normalized wave function is

*Ψ(x,t=0) = √(8/5a) [ 1 + cos(πx/a)] sin(πx/a).*

a) What is the wave function at a later time* t=t0*?.

b) What is the average energy of the system at *t=0* and *t=t0*?

c) Find the probability that the particle is found in the left half of the box (*0≤x≤a*/2) at *t=t0*.

**Solutions**

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