- #1
rwooduk
- 762
- 59
Homework Statement
What are the expansion coefficients of a wavepacket [tex]\Psi (x) = \sqrt{\frac{2}{L}}sin \frac{\pi x}{L}[/tex] in the basis Ψn(x) of a particle in a periodic box of size L?
Homework Equations
[tex]\Psi (r,t) = {\sum_{n}^{}} a_{n}(t) \Psi _{n}(r)[/tex]
The Attempt at a Solution
[tex]\left \langle \Psi _{m}| \Psi \right \rangle= {\sum_{n}^{}} a_{n}(t)\left \langle \Psi _{m}| \Psi_{n} \right \rangle[/tex]
all zero except for m=n therefore
[tex]a_{n}(t)=\left \langle \Psi _{n}| \Psi \right \rangle[/tex]
so I have a term for the coefficients but how do I apply it to the specific wavefunction? espcially as it has no n in it.
Any help as always very much appreciated. Thanks.