(solution) 1.normalize the following wavefunctions: a) sai(x)=sin(3pi/2)

1.normalize the following wavefunctions:

`a) sai(x)=sin(3pi/2) over interval between[0,infinite]`

b) sai(x)=e^-x^2/3 over all x(note: A useful integral is integration from -infinite to inifinite e^-alpax^2 dx=(pi/alpa)^2)).

c) sai(x,y,z)=sin(x)sin(y)sin(z) over x=y=z=[0,pi]

sai(x)=sai1(x)+2sai2(x) are already individually normalized and orthogonal.

2.prove that |sai(x)|^2 is always a real,non negative distribution, which is required if it is to be a probability distribution.