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# quantum mechanics question Watch

1. Can do this but am stuck on part c. How do I do it? Thanks
2. (Original post by importunate)
Can do this but am stuck on part c. How do I do it? Thanks
You can always express the wavefunction using the energy eigenstates as a basis so you have where you can find the coefficients a_n by doing the overlap integral.
3. (Original post by suneilr)
You can always express the wavefunction using the energy eigenstates as a basis so you have where you can find the coefficients a_n by doing the overlap integral.
I have read this in rae but have no idea how to do it... any help? thanks
4. (Original post by importunate)
I have read this in rae but have no idea how to do it... any help? thanks
so

by orthonormality of the energy eigenstates.

5. (Original post by suneilr)
so

by orthonormality of the energy eigenstates.

But I do not know ..
6. (Original post by importunate)
But I do not know ..
well is 1 for n=m and 0 otherwise.

7. What is this though?
8. (Original post by importunate)

What is this though?
It's the complex conjugate of psi_m which in the case happens to be the same as psi_m
9. but I only have phi(x), i know i am missing something silly here... but how the hell do i do this lol
10. (Original post by suneilr)
well is 1 for n=m and 0 otherwise.
Is it?
11. (Original post by importunate)
but I only have phi(x), i know i am missing something silly here... but how the hell do i do this lol
Well m is just some integer. So if you want to find a_1 you do integral psi_1(x) psi(x)dx
12. (Original post by Law123mus)
Is it?
It's the Kronecker delta, no?
13. (Original post by suneilr)
It's the Kronecker delta, no?
Sorry, yes you're right.

$\delta_x=\left\{\begin{matrix}1&\mbox{if}\,\,x=0\\0&\mbox{if}\,\,x\not=0\end{matrix}\right.$
14. (Original post by suneilr)
Well m is just some integer. So if you want to find a_1 you do integral psi_1(x) psi(x)dx
But how do you find a-1 originally?

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