A wave function ψ =A sin (nπx/a) for the motion of a particle in a zero potential well of width ‘a’.?

what you have to do is normalize this wave function

you know that the wave function tells you something about the position of the particle

the probability of finding the particle in a certain region is given by the integral of the square of the wave function, i.e.,

Integral(Ψ*Ψ dx) where the * represents the complex conjugate, but you don't have to worry about that with this function

if you try to find the probability of the wavefunction over the entire space possible, you know that you would get a probability of 1, so...

take your wavefunction, square it, integrate it and set it equal to 1, that will give you the value of A, the amplitude

in other words solve for A:

A^2Integral[Sin^2{nπx/a}dx] =1, limits of integration (0,a)

Hint: remember than n is an integer, so you should get a very simple result for your integral

Well, if not the money, can we at least have some of their jewelry and precious metals. I want a crown made of pure gold, or whatever that thing is that popes wear on their heads.

you use the formula 'x' is the distance since origin;

When you use the computer do not forget that n*Pi*x/a is in radian! so when you calculate the sinus do not forget to use radians and NOT degrees!