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

     \int \psi_m^*(x)\Psi(x) dx = \int \psi_m^*(x) \Sigma a_n \psi_n(x) dx

     \int \psi_m^*(x)\Psi(x) dx = \Sigma a_n \int \psi_m^*(x) \psi_n(x) dx

     \int \psi_m^*(x)\Psi(x) dx = \Sigma a_n \delta_{nm} by orthonormality of the energy eigenstates.

     a_m = \int \psi_m^*(x)\Psi(x) dx
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    (Original post by suneilr)
     \Psi(x) = \Sigma a_n \psi_n(x) so

     \int \psi_m^*(x)\Psi(x) dx = \int \psi_m^*(x) \Sigma a_n \psi_n(x) dx

     \int \psi_m^*(x)\Psi(x) dx = \Sigma a_n \int \psi_m^*(x) \psi_n(x) dx

     \int \psi_m^*(x)\Psi(x) dx = \Sigma a_n \delta_{nm} by orthonormality of the energy eigenstates.

     a_m = \int \psi_m^*(x)\Psi(x) dx
    But I do not know  \delta_{nm}..
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    (Original post by importunate)
    But I do not know  \delta_{nm}..
    well  \delta_{nm} is 1 for n=m and 0 otherwise.
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    \psi_m^*(x)

    What is this though?
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    (Original post by importunate)
    \psi_m^*(x)

    What is this though?
    It's the complex conjugate of psi_m which in the case happens to be the same as psi_m
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    but I only have phi(x), i know i am missing something silly here... but how the hell do i do this lol
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    (Original post by suneilr)
    well  \delta_{nm} is 1 for n=m and 0 otherwise.
    Is it?:confused:
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    (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
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    (Original post by Law123mus)
    Is it?:confused:
    It's the Kronecker delta, no?
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    (Original post by suneilr)
    It's the Kronecker delta, no?
    Sorry, yes you're right.

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    (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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