[Phys-L] Boltzmann function

[Carl Mungan <mungan@usna.edu>]

The current issue of AJP has an article purporting to show an elementary
proof that the Boltzmann distribution function is an exponential. However,
it omits the key step, namely a proof of the fact that the only real
continuous function f that satisfies:

f(x+y) = f(x)f(y)

for independent variables x and y is an exponential. Instead they make
reference to a graduate level math text that has a rather sophisticated
proof. I have attempted to construct a simpler proof of this key step here:

http://usna.edu/Users/physics/mungan/_files/documents/Scholarship/MultiplicativeExponentialProof.pdf

​I invite comments. Even if my proof wouldn't satisfy a mathematician, do
you think it's okay? Can you come up with an even simpler proof?​

​Thanks, Carl

-- 
Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/