Oh, for crying out loud... If it's so, it would take only a minute to say "here's your damn ‹p²›: ...,
My argument is that there is no <p
2> for
any standing harmonic wave. There is though a <k
2> for Sol's standing wave, and if he admits that he cannot calculate this simple integral by himself; I will gladly assist him.
But what he wants me to do is to multiply k, for a standing wave, with (hbar) and then call it momentum. De Broglie's postulate is, HOWEVER, ONLY VALID for a coherent RUNNING wave. Thus, to argue, as Sol wants to argue, that there is also a momentum for a standing wave, and that therefore a standing wave's energy is kinetic energy, violates the physics of harmonic waves.
There is no harmonic standing wave that can have kinetic energy which can be derived from momentum, since there is no standing wave that has momentum; even though a standing wave with a single frequency does have a value for k. So Sol wants to force me to do a calculation in terms of a momentum which makes no physics sense at all when assuming that it is valid for a standing harmonic wave.
TO REPEAT: THERE IS NO STANDING HARMONIC WAVE IN THE UNIVERSE WITH A SINGLE VALUE FOR k WHICH HAS A MOMENTUM PROPORTIONAL TO k; SINCE A STANDING HARMONIC WAVE HAS NO MOMENTUM AT ALL.
In the case of calculating <k
2> the integral is across k
2*[sin(kx)]
2(dx). If Sol cannot do this integral he can ask any high school student to do it for him:
And YES it is not zero: but it has NOTHING to do with momentum since, to repeat for the 100th time: A STANDING WAVE DOES NOT HAVE MOMENTUM.
ONLY A RUNNING ELECTRON WAVE HAS MOMENTUM AND ONLY IN THIS CASE DOES DE BROGLIE'S RELATIONSHIP APPLY. WHY WOULD THE HARMONIC WAVE MODELLING AN ELECTRON BE DIFFERENT FROM ALL THE OTHER HARMONIC WAVES EVER KNOWN WHICH ARE MODELLED BY THE SAME MATHEMATICS?