Now Alex, that is a matter of opinion! The origin of the value of Plank's constant is not known yet by you! The origin of the exact value of both Plank's constant and the speed of light is known by me. And it could be known by you if you would follow my development of Quantum Mechanics carefully. The value of these constants turns out to be what they are because the physics community has over specified it's definitions: i.e., they have not carefully considered the full consequences of earlier definitions of their fundamental concepts.
If you go to my presentation, which defines each concept but a single time, you will find that I show that equation 2.15 must be valid in all possible concepts of reality. "q" and "k" in that equation are nothing more than totally arbitrary numbers. In expression 2.16, I define three variables: m is defined to be q times h bar over c (which means m is as arbitrary as q: i.e., no constraints what so ever have been imposed), c is defined to be 1 over k times the square root of 2 (which means c is as arbitrary as k: i.e., again, no constraints what so ever have been imposed) and finally, V(x) is defined to be minus the quantity (h bar times c divided by 2q) times g(x), g(x) being the result of an integration defined earlier. These are all totally arbitrary definition and contain no physics per se.
Please note that at this point in my work, no meaning what so ever has been attached to any of these numbers. Not only that but neither mass nor energy have been defined at all so I am free to give them any definitions I wish! (c is related to k which I discuss at a later date; for the moment let us concern ourselves with h bar).
When I take the above definitions and multiply equation 2.15 through by minus h bar over c, I get equation 2.17, Schrodinger's equation in one dimension. Multiplying any equation through by any constant in no way fixes the value of the constant.
So how did h come to have the value it has? Scientists have over defined the variables. Momentum is defined at least twice: once as "mass times velocity" (remember, mass was long ago defined in terms of forces another rather anthropromorphicly defined term) and secondly as proportional to a differential operator with regard to the probability of seeing the event. In my opinion, the second definition (as a differential operator) is much more basic.
The first is better seen as a consequence of solutions to the differential equation as Quantum Mechanics (as I have derived it) cannot fail to be true!
If you would follow my development line by line instead of jumping to the conclusion that I am doing is something which has already been done (treat it as you would a mathematical problem) I think you might understand what I am doing.
I am truly sorry that I have been unable to reach you.
Yours -- Dick
PS If you don't think h bar is circularly defined, go take a look at the book "Mr Tompkins goes to Quantum Land" (which is clearly erroneous) and then try to describe a world where h bar has a value a million times larger and everythine else you know about physics is correct!
The book should be in your University Library, if it isn't tell them to see if they can borrow a copy from Vanderbilt. I know they have a copy.