> >From: Russell Standish <R.Standish.domain.name.hidden>
> >Basically, the i in the equation is to ensure that the Hamiltonian is
> >hermitian, which is required by the law of conservation of probability
> >(d/dt (psi* psi))=0. This latter law is simply the statement that the
> >axiom saying the probability of the certain event is 1, and shall
> >remain so for all time.
>
> As you know Russell, I find your "derivation" of the SE quite wanting.
> As far as conservation of probability, it is not obvious that measure should
> be conserved as a function of time. In fact, measure is not strictly
> conserved.
> The i is there to make the equation simpler to write. Of course one
> could write it in terms of real quantities only, such as amplitude and
> phase.
Well wait for the mark 2 version of the Occam paper, where I shall be
far more explicit in the steps. Sorry it is taking so long, but I have
a real job to do as well.
One of the Kolmogorov probability axioms is that the certain event has
probability 1. Conservation of probability is simply asserting that
the probability of the certain event does not change over time. A
fairly obvious corrollory one would have thought.
Saying that the i is there makes it easier to write misses the
point. The Schroedinger operator is i times a Hermitian operator. This
is not the most general form of linear operator, so this structure
ought to have some form of explanation. The one I gave is not actually
due to me, but I can't think where I first came across it - possibly
Emile Durand.
>
> - - - - - - -
> Jacques Mallah (jackmallah.domain.name.hidden)
> Physicist / Many Worlder / Devil's Advocate
> "I know what no one else knows" - 'Runaway Train', Soul Asylum
> My URL: http://hammer.prohosting.com/~mathmind/
>
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>
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Dr. Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967
UNSW SYDNEY 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Sun Jun 25 2000 - 17:33:17 PDT