planck's constant

Kraig Grady asks:

>I am hoping someone can answer this question. If planck constant states
>that energy states can exist only in discrete steps does this apply to
>Frequency generated by a single physical system. In other words is a
>glissando not a glissando but minute little steps whole number multiples
>of a vibration detated by Planck Constant.If so, what is the octive
>equivalent of this fundamental?!

My physics is a bit rusty, but quantum mechanics doesn't work this way. Some
systems have nice discrete energy levels, other systems have continuous levels,
other systems have a combination of the two. Seems like it's when a system has
some kind of boundary that the discrete levels arise. This is just like a
conventional oscillating system like a string. An infinitely long string would
not have an overtone series, it could vibrate at any frequency. Put ends on
the string, now you have a discrete set of modes of oscillation.

The bounds don't have to be so fixed though. A simple oscillator like a mass
and a spring, that's the classic example of a system with discrete energy
levels, all nice and evenly spaced just like an overtone series. The hydrogen
atom is another classic. It has a bunch of unevenly spaced discrete levels for
the states where the electon is in a bound orbit, and then a whole continuous
range of levels where the electron is wandering around unbound.

My first introduction to quantum mechanics was from a book my high school
chemistry teacher (Mr. St. John, really a great inspiration in my life) loaned
me. It had a bunch of pictures that made the analogy between quantum systems
and classical oscillating systems like drum heads. I think your basic
intuition, that the discrete levels of quantum systems have some connection to
music, is correct. Of course the devil is in the details!

Jim


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