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Quantum mechanics: Schrodinger equation help watch

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    I have this example:
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    I understand it up until the sentence starting "Comparing this to the known". How did my lecturer get from the trig equation in the centre to the series? Where did npix/L come from in that? Also where do a1, a2 and an come from?
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    Those are the possible eigenfunctions for the infinite square well Hamiltonian.

    To get them you solve the Schrodinger equation for that potential, and you get those as the possible solutions. A general wave function can then be expanded as a series of those solutions (with complex coefficients, the magnitude of which is the probability of obtaining that result in a measurement).

    The infinite square well (or 'particle in a box' for higher dimensions) is a really fundamental problem. I'm sure any book (or site) on quantum mechanics will cover it in detail.
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    The series expansion comes from using the binomial for the exponential form of sin x. Do the piecewise addition and the general term drops out.
 
 
 
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Updated: April 15, 2013
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