Question

(a) One of the solutions of the Schrödinger equation for a particle of mass m
experiencing a potentialV  kx2 1
2
, k being constant is
2     x Axe . Find out the value
of  and the energy.
(b) Find the value of o x  x , beyond which the region is classically forbidden for the
particle.
(c) Consider a particle bound between o o x  x  x in the following potential
2 1
2
  
    
  
for
for
for
o o
o o
o o
V V x x
V kx x x x
V V x x
Can
2     x Axe still be a valid wave function for the region o o x  x  x ? Please
give precise reasons.