- #1

kcirick

- 54

- 0

**Question:**

A particle of mass m moves in 1-D infinite square well. at t=0, its wave function is [itex] \Psi\left(x,t=0\right)=A\left(a^{2}-x^{2}\right)[/itex]. Find the probability that the particle is in the energy eigenstate [itex]E_{n}[/itex]. Does the probability change with time?

**What I have so far:**

So far I just found the normalization constant for the wave function at t=0:

[tex]\int|\Psi\left(x,t=0\right)|^{2}dx=1[/tex]

[tex]...A=\frac{1}{4}\sqrt\frac{15}{a^{5}}[/tex]

So we have [tex] \Psi\left(x, t=0\right)=\frac{1}{4}\sqrt\frac{15}{a^{5}}\left(a^{2}-x^{2}\right)[/tex]

Now, because this is infinite square well, [itex]\Psi=0[/itex] at the boundary. From that, we can find out the energy eigenstate:

[tex]E_{n}=\frac{n^{2}\hbar^{2}\pi^{2}}{8ma^{2}}[/tex] (Derived in class)

But what to do from there? I don't know...