Thread: how to find the coefficient of wavefunctin of infty square well

1. how to find the coefficient of wavefunctin of infty square well

if we know $\displaystyle \psi(x,0)=cx(a-x)$

how to find c

2. I guess the well has borders at 0 and a. Hence we know (with 100% probability) that particle is inside the well. Thus probability that particle is inside the well is 1:
$\displaystyle \int_{0}^{a} \bigl|\psi(x)\bigr|^2dx = 1$

We get
$\displaystyle c^2 \int_{0}^{a} x^2(a - x)^2 dx = 1$

3. Originally Posted by silversand
if we know $\displaystyle \psi(x,0)=cx(a-x)$

how to find c
There may be several ways to determinate $\displaystyle c$ with respect to the initial conditions.
There may be several ways to determinate $\displaystyle c$ with respect to the initial conditions.
I disagree. I've showed the way to calculate c, frankly speaking what we have here is an initial condition. We can calculate $\displaystyle \psi(x, t)$ expressing $\displaystyle \psi(x, 0)$ as linear combination of eigenfunctions.