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Eigenfunction, Eigenvalue, Wave Function and collapse

  1. Dec 29, 2007 #1
    Reading Sam Treiman's odd quantum he nicely explains the dependencies between the Schrödinger wave equation, eigenvalues and eigenfunctions (page 86 onwards). In his notation, eigenfunctions are [itex]u:R^3\to R[/itex] and the wavefunction is [itex]\Psi:R^4\to R[/itex], i.e. in contrast to the eigenfunctions it depends on time.

    Then on page 94 he says:
    With "state of the system" he refers of course to [itex]\Psi[/itex], so during the measurement, the jump or collapse is from [itex]\Psi[/itex] to [itex]u[/itex].

    The one thing I don't understand here is: [itex]u[/itex] does not depend on time, so how is the development of the new [itex]\Psi[/itex] over time governed? Is it that every solution of the Schrödinger equation is uniquely determined as soon as the value at just one point in time is known?

    Harald.
     
  2. jcsd
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