sci.physics.research

On 4 Aug., 05:51, Igor Khavkine wrote:
> More precisely, this "rule" states that the
> eigenvalues of J will be discrete and, for large n, will have the form
> J_n ~ h (n+w) + O(h^2), where w is a corrective constant originally
> ignored by Sommerfeld and Wilson. The proof of this asymptotic formula
> is given through the WKB approximation, wich also allows one to compute
> the O(h^2) and higher order expansion terms.
>
> For the simple harmonic oscillator, w = 1/2, the O(h^2) terms happen to
> identically vanish and the action variable J is proportional to the
> total energy, yielding the well known energy spectrum E = h-bar omega
> (n+1/2). Any text which explains the WKB approximation gives many more
> examples.
>
> I hope this explanation underscores the importance of context when
> trying to interpret or use any particular "law" or "rule" in physics.
>
> [1] Fetter & Walecka, Theoretical Mechanics of Particles and Continua,
> Dover (2003).
> [2] Goldstein, Classical Mechanics (2nd ed.), Addison-Wesley (1980).
>
> Igor

This cannot be the full truth. Any real measurement device
will measure action in units of h, so how should it be able to
give a result that is, say, h?

It is not possible to measure action values that are fractions of h
in nature (put in a factor 2 pi for a precise statement).

I challenge Igor to provide any experiment where an action value
smaller than h has been measured. (I am not talking about
experiments where large action values are divided by particle numbers;
the large action value is always an integer multiple of h.)

Optics or particle detection, etc always provide integer
multiples of h. (And of course, at macroscopic values of the action,
measurement errors make any statement impossible.)

For my university teachers it has always been clear that all
measured action values are spaced by h.

On the other hand, what Igor states somehow must also
be correct. It is just that I do not have the reference at hand.
But the literature on the eigenvalues of the "action operator"
is sparse; it would be great if more details would be
available online somewhere. We could check the
assumptions on those calculations.

John