Richard,

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

• You insult me - yanniru - May 10, 2002 - 21:12 UTC
  • Sorry about that 7 years at Harvard! - doctordick - May 11, 2002 - 12:49 UTC
    • Sorry - yanniru - May 11, 2002 - 16:20 UTC
      • Yanniru: a question - dolphin - May 11, 2002 - 22:59 UTC
        • Yanniru, further on the above - dolphin - May 12, 2002 - 00:49 UTC
          • And note Aurino's comment - dolphin - May 12, 2002 - 01:19 UTC
            • Responding to Aurino - yanniru - May 12, 2002 - 18:44 UTC
      • ????? - doctordick - May 13, 2002 - 01:05 UTC
        • I agree with John Anderson and Eric Preby - bruce - May 13, 2002 - 05:37 UTC
          • Too bad they didn't give a thorough response - harvey1 - May 13, 2002 - 14:26 UTC
            • Too bad, indeed - pmartin - May 13, 2002 - 15:45 UTC
              • Science has already solved Dick's problem - yanniru - May 13, 2002 - 15:56 UTC
                • It could be - pmartin - May 13, 2002 - 16:17 UTC
                  • It's all math - yanniru - May 13, 2002 - 22:58 UTC
                    • "Our" longest sustained topic ever here thus settled? - occupant - May 14, 2002 - 07:27 UTC
                    • I think your insight is as keen as your wit, Mike (nt) - pmartin - May 15, 2002 - 23:03 UTC
                      • Although I'm residential, I'll pass along your remarks to Mike - occupant - May 15, 2002 - 23:26 UTC
              • Pythagorean nonsense - harvey1 - May 13, 2002 - 16:52 UTC
                • some kind of nonsense, for sure - occupant - May 14, 2002 - 07:11 UTC
            • A wave equation - yanniru - May 13, 2002 - 15:49 UTC
              • I need to review this - harvey1 - May 13, 2002 - 19:10 UTC
                • I am pleased that Dick sticks to his guns - yanniru - May 14, 2002 - 21:20 UTC
                  • you were quite unsuccessful refuting MY points - occupant - May 16, 2002 - 05:18 UTC
            • 'Political' science....I don't think Dr. Dick seeks "adherents" - occupant - May 13, 2002 - 16:30 UTC
              • It's not "it's flinger" of course; it's "its flinger." - occupant - May 14, 2002 - 04:55 UTC
            • Harv - bruce - May 14, 2002 - 14:50 UTC
              • I agree the response was warranted - harvey1 - May 14, 2002 - 15:11 UTC
            • Harv - bruce - May 14, 2002 - 14:52 UTC
              • ridiculous comments do not augment science writing - occupant - May 14, 2002 - 15:48 UTC
                • They are much easier... - bruce - May 15, 2002 - 14:23 UTC
                  • sly, clever - something - May 15, 2002 - 15:38 UTC
                    • I agree with.. - bruce - May 16, 2002 - 03:31 UTC
                      • So a metaphor is not ridiculous even if far from exact? - occupant - May 16, 2002 - 05:51 UTC
                        • I agree with Patrick and Bilge... - bruce - May 16, 2002 - 20:29 UTC
                          • thanks, you took the easier questions and left the others to - occupant - May 16, 2002 - 21:30 UTC
                            • Not sure what you are getting at... - bruce - May 16, 2002 - 23:48 UTC
                              • nibbling around at the topics - occupant - May 17, 2002 - 04:14 UTC
                                • Tell me what you think wrt universal time... - bruce - May 17, 2002 - 04:49 UTC
                                  • Universal may be like relative time but context frame bigger - spazcon - May 17, 2002 - 19:11 UTC
                                  • Were you going to reply this year? - carefuluniverse - June 6, 2002 - 16:21 UTC
                          • I agree with myself - occupant - May 16, 2002 - 23:44 UTC
        • Equation 5.3 - yanniru - May 13, 2002 - 14:25 UTC
          • A note on rigor - pmartin - May 13, 2002 - 16:04 UTC
            • Isomorphisms - yanniru - May 13, 2002 - 23:05 UTC
• Where did you go to school(nt) - yanniru - May 10, 2002 - 21:13 UTC
  • It was a reputable school! - doctordick - May 11, 2002 - 15:48 UTC
    • As I said above - yanniru - May 11, 2002 - 16:10 UTC
• Did you graduate( - yanniru - May 10, 2002 - 21:14 UTC
  • Yes! - doctordick - May 11, 2002 - 17:06 UTC
    • You're a good guy - harvey1 - May 11, 2002 - 21:05 UTC
      • I loved it! - doctordick - May 12, 2002 - 03:42 UTC
        • Hmm... - harvey1 - May 12, 2002 - 14:48 UTC
          • Didn't see Spiderman yet - yanniru - May 12, 2002 - 18:49 UTC