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Basis function method

  1. Feb 28, 2005 #1
    Psi(x) = Sumationn CnPhin(x)

    in order to find Cn, i have to multiply both side of the above equation by Phi*k(x) and take the integral. The result is Ck if n = k. My question is what is the value of Phi*k(x)?

    i know that multiplying both side of the equation by Phi*k(x) would make the function orthonormal when n != k, and normalize when n = k. But i don't know how to find it.
     
  2. jcsd
  3. Mar 1, 2005 #2

    dextercioby

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    Is this:[tex]\psi(x)=\sum_{n}C_{n}\phi_{n}(x) [/tex](1)...?

    Is the basis [tex] \{\phi_{n} \}_{n=1}^{\infty} [/tex] orthonormal...?If so,then multiply (1) by [itex] \phi_{k}^{*}(x)[/itex],sum after "k" & integrate after "x"...

    Daniel.
     
  4. Mar 1, 2005 #3
    what is the condition for [tex] \{\phi_{n} \}_{n=1}^{\infty} [/tex] to be orthonormal? thanks
     
  5. Mar 1, 2005 #4

    Galileo

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    Per definition, if the following holds, the set [itex]\{\phi_{n} \}_{n=1}^{\infty}[/itex] is orthonormal:

    [tex]\langle \phi_i|\phi_j\rangle = \int \limits_{-\infty}^{+\infty}\phi_i^*(x)\phi_j(x)\; dx=\delta_{ij}[/tex]
     
  6. Mar 1, 2005 #5
    can you provide an example?
     
  7. Mar 1, 2005 #6

    dextercioby

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    Hidrogenoid functions are an interesting example.SHO eigenfunctions are other example.Rigid rotator is another example.Infinite square well and so on,and so forth.

    Daniel.
     
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