Originally Posted by johanfprins:
Then do it.
Zig: That's not the deal, johan.
I'll do half the calculation, IF you promise to do the other half. You even get to pick which half, <V> or <p2>/2m.
It is not a question of not being able to do any of the two calculations, but a refusal on my part to calculate parameters which have no physics-meaning whatsoever.
Or admit that you can't, and I'll do the whole thing.
I know that you can do the whole thing and is willing to do so. Why not: You have posted so many comments which are not physics. Go ahead and calculate two parameters which are also not physics. But I refuse to play a role in calculating paranormal physics.
JFP: Well we know that we need a photon of approximately 13.7 eV to break up a hydrogen atom.
Zig:But you can't predict this number, can you? You can't calculate this energy. You can't tell me why it's 13.7, not 13.8, or 26.4, or any number, can you?
Amazingly I can calculate this number to an excellent approximation by using the Schroedinger equation and inserting the classical potential field between an "electron-particle" and a "proton particle". Why this is possible nobody knows since the Schroedinger equation has been a guess.
After solving the equation, the solution is, however, a standing wave with zero momentum and zero kinetic energy, having an energy of approximately 13.7 eV below the vacuum level. This is the same as the mass-energy that has been radiated away: And therefore the hydrogen atom has a mass of M
H=m
P+m
e-MINUS-13.7(eV)/c
2 without any "internal" kinetic energy.
JFP: Now go ahead and calculate the masses (delta)mp and (delta)me as you claim that you can do.
Zig: Not until you agree to my terms above. They're quite fair.
They are not fair since you want me to calculate parameters which are not physically relevant. As a realistic physicist I protest.
JFP:
The solution derived from Schroedinger's equation for Sol's famous standing waves in a box
Zig: This is the hydrogen atom we're talking about. The solution isn't the wave Sol gave for the particle in a box.
It does not matter which solution you take: The parameters you want me to calculate, has no physical meaning at all.
JFP: gives the energies En=(hbar*kn)2/me)-V, which must be interpreted as an approximation for (delta)mP+(delta)me: So where is your kinetic energy?
Zig: It's +V, not -V (though V may be negative).
According to the text books and according to you I can choose to measure the potential energy from any level? Or do you agree with me that in the case of the Schroedinger equation this must not be done since the only valid reference level is the vacuum level: If the latter is correct, and it must be correct, then the potential well within which an electron becomes trapped when it bonds to a nucleus, or within a material for that matter MUST always be negative.
And there's no k anywhere in the hydrogen atom solution.
Any harmonic wave, and a Schroedinger wave is a harmonic wave, "lives" within both position space and k space (reciprocal space) simultaneously. To go from one space to the other one uses a Fourier transform. Thus if you have the wave-function within position space, you can always calculate <k> and <k
2> for any Schroedinger wave-function. There are then three possibilities:
1. <k>=k and <k
2>=0: In this case you have a travelling coherent wave moving past with a momentum p which relates to k by de Broglie's relationship p=(hbar)*k.
2. <k>=0 and <k
2> NOT EQUAL TO 0. In this case you have a standing wave without any momentum and without any kinetic energy. Although you can still use (hbar) to write p=(hbar)*k this expression is now physically meaningless since it cannot be a momentum.
3. <k>=k
0, with <(k-k
0)
2> NOT EQUAL TO zero. In this case you have a wave packet that moves with a group velocity which cannot be derived from the “momentum” (hbar)*k
0. Thus also in this case the expression p=(hbar)*k0 is meaningless since it does not relate to an actual momentum.
JFP: What calculation do you want me to do?
Zig: Either <p2>/2m or <V> for the ground state of hydrogen, take your pick. I'll even do the other one first, if you agree to do one of them.
I told you that I refuse to calculate parameters which have no physics-meaning. You want to argue that the first expression proves that there is kinetic energy. According to Ehrenfest’s theorem you have that:
<F>=(d/dt)<p>: Thus for a distance ds one must have that:
<F>ds=(ds/dt)*d<p>=<v>*d<p>= (1/m)*<p>*d<p>
If you now integrate to get the kinetic energy you get <p>2/2m AND NOT <p2>/2m.
Similarly, once quantum mechanical bonding has occurred, the classical potential energy plays no role anymore. Thus to calculate <V> is paranormal nonsense. The physics in which you, Sol, Ben and your choir specialise in.