I'm trying to get my head around the idea of expansion coefficients when describing a wavefunction as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Psi(\textbf{r}, t) = \sum a_{n}(t)\psi_{n}(\textbf{r})[/tex]

As I understand it, the expansion coefficients are the [tex]a_{n}[/tex] s which include a time dependence and also dictate the probability of obtaining an eigenvalue whereby [tex]\sum |a_{n}(t)|^{2} = 1[/tex]. I also understand that the expectation values of operators can be given as function of the [tex]a_{n}(t)[/tex] coefficients given the orthonormality in the eigenfunctions, whereby [tex]<H> = \sum |a_{n}(t)|^{2} E_{n}[/tex].

If I'm looking at the wavepacket:

[tex]\psi(x) = \sqrt{\frac{2}{L}}sin(\frac{\pi x}{L})[/tex]

How would I determine the expansion coefficients of the wavepacket in the basis states [tex]\psi_{n}(x)[/tex] for the particle in the periodic box, length L? I'm completely confused about the terminology here.

Any help/explanation would be massively appreciated

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# Homework Help: Wavepacket expansion coefficients

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