Quantum question

[Eeezee]

Not sure if this is the best place to ask, but it's the only AT forum that should fit.

Does the wave function for a particle in an infinite voltage well always reduce to a A*sin(kx) formula? I understand that it's like a wave on a string in the sense that you can only have an integer number of nodes (n=0,1,2,3....).

The reason I ask is that I've been asked to normalize a wave function for such a particle, only the equation is as follows

f(x,t=0) = A(psi_1(x) + (e^(i*theta))*psi_2(x))

I'm assuming that psi_1 and psi_2 are the wave function for n = 1 and n = 2, where psi = C*sin(n*pi*x/a) and a is the length of the well.

Also, how would I find the complex conjugate for psi_1 or psi_2? I have only ever taken a complex conjugate for functions with complex powers (such as e^(a+ib), the complex conjugate is e^(a-ib)). I made another assumption here, which is probably wrong, but I decided that the complex conjugate of sin(n*pi*x/a) should just be the same function sin(n*pi*x/a)

Any help appreciated, thanks 🙂

 

[f95toli]

Yes, they do.
Psi_1 and Psi_2 are the wavefunctions for the ground- and first excited state.
The complex conjugate for a real function f(x) is just f(x), so your assumption is correct.

 

[iwantanewcomputer]

complex conjugate for psi_1 + i*0 is psi_1 - i*0

the rest confuses me...and i'm reading a QM book now 🙁

 

[Eeezee]

Kickin', that's exactly what I wanted to know. Thanks a bunch =)