source file: mills3.txt Date: Mon, 29 Dec 1997 18:13:45 +0100 Subject: planck's constant From: James Kukula 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 SMTPOriginator: tuning@eartha.mills.edu From: Carl Lumma Subject: Top Ten PostedDate: 29-12-97 18:26:07 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 29-12-97 18:23:46-29-12-97 18:23:47,29-12-97 18:23:11-29-12-97 18:23:12 DeliveredDate: 29-12-97 18:23:12 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C125657C.005F8D70; Mon, 29 Dec 1997 18:25:37 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA26747; Mon, 29 Dec 1997 18:26:07 +0100 Date: Mon, 29 Dec 1997 18:26:07 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA26135 Received: (qmail 24533 invoked from network); 29 Dec 1997 09:26:03 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Dec 1997 09:26:03 -0800 Message-Id: <19971229172634031.AAA220@ascend558.nni.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu