Re: quantization

[Leigh Palmer <palmer@sfu.ca>]

Dorry, Luwik; I intended to answer your question earlier,
but I must have lost it. In the hope that late is better
than never...

> > .... Charge is quantized; energy is not....
>
> This calls for an elaboration. We do teach about energy levels in
> molecules and atoms. What is quanized by the principle quantum number
> n in the theory of hydrogen atom? Are some forms of energy quantized
> whil others are not? I am probably missing something important.

If the state of an isolated system can be characterized
by stationary solution to Schrodinger's equation then the
energy of that system can take on only a discrete set of
values. The enrgy of the system is said to be quantized.

Energy is not an entity capable of existence independent
of some physical system; it is a canonical attribute of
any given system. Once one finds the rule (the canon, or
law) which adequately describes the energy attributable
to a given system than one may use that system as part of
a larger system and reckon its energy as part of the
energy of the larger system using the rule as an additive
term.

Energy is an abstract physical quantity; there is no such
thing as "pure energy". If the system under consideration
has energy levels sufficiently closely spaced (delta E)
andthea relaxation times sufficiently short (delta t),
then the uncertainty products (delta E x delta t) will
always be smaller than the minimum under the uncertainty
principle (h-bar/2) necessary for the meaningful
establishment of a stationary state. Under such
circumstances even the energy of an isolated system is
not quantized.

Problem: Given that the maximum delta t achievable is
less than 5 x 10^17 s (the age of the universe) what is
the largest conceivable isolated system that could
meaningfully be considered capable of being in a
stationary state?

Leigh