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Posted by Richard D. Stafford, Ph.D. on May 10, 2002 15:58:42 UTC


Have you ever done any math with the Dirac delta function?

From the characteristics of your posts, I get the distinct impression that you do not know how to do an integral over an expression containing a Dirac delta function. The Dirac delta function is defined by a limiting process, but, in layman's terms, it's shape can be thought of as in infinite spike when the argument is zero and zero everywhere else with the important characteristic that an integral over the entire range of the argument is exactly 1 (of course, integration over any part away from zero is unimportant but we can leave it in anyway).

The consequence of this is that the integral over any function times the Dirac delta function yields exactly that other function evaluated when the argument of the Dirac delta function is zero. Now, if the argument of the Dirac delta function is xi-xj then all the integral over xj accomplishes is that it picks up the remainder of the stuff under the integral with xi substituted for xj everywhere.

That is elementary work with Dirac delta function!

***** Yanniru
The fact that F always equals zero carries through to V(x) always equaling zero if you use the delta function.

F=0 is the equation which enforces the rule imposed by our "unknowable" data. That is, when the data satisfies the equation F=0 it is valid data! The important characteristic here is that when the data does not satisfy F=0 then it is not valid data! If it is not valid data, then the probability of seeing it must be zero (invalid means it can't happen). Well, gee whiz guys, that means that every time F is not zero, psi is zero. It follows, as the night the day, that the product F*psi is always zero and it doesn't make any difference at all what the arguments of the functions are!!

Again Richard, this is elementary stuff!!

Looking to hear from you -- Dick

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