Normandy6644

2005-Mar-03, 04:56 AM

Okay, so I've been dealing with wavefunctions and the solutions to Schrodinger's Equation lately. Here's something I have to do this week:

If the wave function in an infinite potential well is initally given by Psi(x,0)=sin(pi*x/L) + B*sin(3pi*x/L)

a) find the constant B

b) find the time-dependent wavefunction Psi(x,t)

c) Determine after which time the wave function has the same form, i.e. for what T is Psi(x,T) = Psi(x, 0)

For part a, it seems like what I have to do is normalize Psi, which I did and got an answer of (3pi/2L)-3 for B. I'm not 100% sure that's what I was supposed to do, but I couldn't think of anything else at the time.

For b, I'm thinking I'm supposed to use the general form for Psi(x,t) as a sum over the spatial functions and use some orthogonality condition to solve for the constants. Not exactly sure how to do that though...

Part c seems like it will follow easily after I nail down b.

Naturally, I'm not looking for answers, only a push in the right direction. :D

If the wave function in an infinite potential well is initally given by Psi(x,0)=sin(pi*x/L) + B*sin(3pi*x/L)

a) find the constant B

b) find the time-dependent wavefunction Psi(x,t)

c) Determine after which time the wave function has the same form, i.e. for what T is Psi(x,T) = Psi(x, 0)

For part a, it seems like what I have to do is normalize Psi, which I did and got an answer of (3pi/2L)-3 for B. I'm not 100% sure that's what I was supposed to do, but I couldn't think of anything else at the time.

For b, I'm thinking I'm supposed to use the general form for Psi(x,t) as a sum over the spatial functions and use some orthogonality condition to solve for the constants. Not exactly sure how to do that though...

Part c seems like it will follow easily after I nail down b.

Naturally, I'm not looking for answers, only a push in the right direction. :D