Expanding Wavefunction in Infinite Well: Fourier Analysis

[ehrenfest]

I have an infinite well from -a to with a particle in its ground. The initial wavefunction is then

$$\psi(x) = u_1^+(x;a) = cos(\pi x/ 2a)/\sqrt{a}$$ for |x| < a.

In order to get the wavefunction for this particle when box that is instantaneously expanded to [-b,b] should I apply Fourier analysis via

$$a^{+}_n = 1/b \int_{-b}^{b}cos(\pi x/ 2a)/\sqrt{a}\cdot cos(\pi x/ 2b)/\sqrt{b}dx$$

where a^{+}_n is the coefficient of the even wavefunction with that n in the expanded box?

 

[Meir Achuz]

Yes, then put in the time dependence.