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birulami
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Reading Sam Treiman's http://books.google.de/books?id=e7fmufgvE-kC" 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.
Then on page 94 he says:
Whatever the state of the system was just before the measurement, during the measurement process it "collapses" into the eigenstate [itex]u[/itex] that corresponds to the eigenvalue [itex]\lambda[/itex] obtained in the measurement.
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.
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