- #1

Zack K

- 166

- 6

- Homework Statement
- A particle is in a one-dimensional infinite square well potential of width ##a## such that:

##V(x)=0 ## for ## 0\leq x\leq a## and ##V(x)=\infty## otherwise. At ##t=0##, the particle has wave function ##\psi(x,0)=Ax(a-x)## for ##0\leq x\leq a##. Determine the constant ##A## to normalize the wave function.

- Relevant Equations
- ##\int_{-\infty}^\infty \psi*_n\psi_n dx=1##

Some questions:

Why is this even a valid wave function? I thought that a wave function had to approach zero as x goes to +/- infinity in all of space. Unless all of space just means the bounds of the square well.

Since we have no complex components. I am guessing that the ##\psi *=\psi##.

If this is true, how do I evaluate the integral for quantum number n? I first chose n=1 then evaluated the integral and managed to normalize it. But if I evaluate for ##\psi_n##, I get a nasty function which did not normalize. is it wrong that ##\psi_n=A_nxn(a-xn)?##

Why is this even a valid wave function? I thought that a wave function had to approach zero as x goes to +/- infinity in all of space. Unless all of space just means the bounds of the square well.

Since we have no complex components. I am guessing that the ##\psi *=\psi##.

If this is true, how do I evaluate the integral for quantum number n? I first chose n=1 then evaluated the integral and managed to normalize it. But if I evaluate for ##\psi_n##, I get a nasty function which did not normalize. is it wrong that ##\psi_n=A_nxn(a-xn)?##