1 Dimentional Schrodinger equation

[budafeet57]

Homework Statement

Consider the one dimensional wave funciton give below.
a) Draw a graph of the wave function for the region defined.
b) Determine the value of the normalization constant
c) what is the probability of finding the particle between x = 0 and x = a/2
d) show that the wave function is a solution of the non-relativistic wave equation (Schrödinger equation) for the potential energy function give below.
ψ(x) = A(a^2-x^2) for -a < x < +a
ψ(x) = 0 for x< -a and x > a
U(x) = -((h bar)^2/ma^2)(x^2/(a^2-x^2))

Homework Equations

shown above

The Attempt at a Solution

a)

b)

a
∫ ψ(x)^2 dx =1
-a

a
∫ (A(a^2-x^2))^2 dx = 1
-a

A = (√15 )/4√a^5

c)
39.4%

d)I was given the question without answer, some help verifying my answer would be appreciated!

 

[budafeet57]

for part d, do I just do this?: