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Quantum mechanics: Schrodinger equation help watch

    • Thread Starter

    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?

    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.
    • Study Helper

    Study Helper
    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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