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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

Normandy6644
2005-Mar-03, 10:37 PM
Nevermind. :D Forgot to square the wavefunction before normalizing! #-o

Normandy6644
2005-Mar-04, 01:43 AM
I've figured out A and B, but C is being more of a pain than I would have hoped. Anyone have any ideas?

Grey
2005-Mar-04, 03:16 AM
I've figured out A and B, but C is being more of a pain than I would have hoped. Anyone have any ideas?
If you've worked out the time dependence, that should give you a period, shouldn't it? Can you give me the answer to part B?

Normandy6644
2005-Mar-04, 04:48 AM
I've figured out A and B, but C is being more of a pain than I would have hoped. Anyone have any ideas?
If you've worked out the time dependence, that should give you a period, shouldn't it? Can you give me the answer to part B?

Sure. I have that

Psi(x,0)=sin(x*pi/L)exp(-iwt)+sqrt[(2/L)-1]sin(3*pi*x/L)exp(-9iwt)

where w=(hbar^2)(pi^2)/(2*m*L^2).

Grey
2005-Mar-04, 06:00 AM
Sure. I have that

Psi(x,0)=sin(x*pi/L)exp(-iwt)+sqrt[(2/L)-1]sin(3*pi*x/L)exp(-9iwt)

where w=(hbar^2)(pi^2)/(2*m*L^2).
So you have two functions that vary in space (we don't really care how). They also both vary in time, one with a frequency of w, the other with a frequency of 9w. What's the smallest value of t that would leave both exp(-iwt) and exp(-9iwt) the same value as exp(0)?

Normandy6644
2005-Mar-04, 12:51 PM
Sure. I have that

Psi(x,0)=sin(x*pi/L)exp(-iwt)+sqrt[(2/L)-1]sin(3*pi*x/L)exp(-9iwt)

where w=(hbar^2)(pi^2)/(2*m*L^2).
So you have two functions that vary in space (we don't really care how). They also both vary in time, one with a frequency of w, the other with a frequency of 9w. What's the smallest value of t that would leave both exp(-iwt) and exp(-9iwt) the same value as exp(0)?

Oh wow, I'm so blind. I forgot that those were imaginary exponents!! #-o

Grey
2005-Mar-04, 03:35 PM
Oh wow, I'm so blind. I forgot that those were imaginary exponents!! #-o
Ah, yes, that would do it. Glad I could help. :)

Normandy6644
2005-Mar-04, 06:16 PM
Oh wow, I'm so blind. I forgot that those were imaginary exponents!! #-o
Ah, yes, that would do it. Glad I could help. :)

Thank you! :D