source file: mills3.txt Date: Tue, 30 Dec 1997 08:27:23 +0100 Subject: quantum mechanics From: James Kukula Thinking a bit more about quantum mechanics and oscillators... the problem of the quantum behavior of a vibrating string is essentially the same as the problem of electromagnetic radiation in a cavity, the thermodynamic aspect of which led Planck to his original hypothesis at the very origin of quantum mechanics, back around 1900. Classically we would describe the motion of a string by providing amplitudes and phases for each of the modes of osciallation. As the string is coupled to its environment, these amplitudes would slowly and steadily decrease as the string vibrates a sounding board which radiates the sound. Quantum mechanically, each mode of oscillation would not have a continuous range of possible amplitudes, but a discrete range. These amplitudes would not steadily decrease, but somehow they jump discretely from one amplitude level to a lower level. So it's the diminuendo, not the glissando, that gets broken into minute steps! Jim SMTPOriginator: tuning@eartha.mills.edu From: Aline Surman Subject: Wilson scale PostedDate: 30-12-97 08:42:36 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: 30-12-97 08:40:20-30-12-97 08:40:20,30-12-97 08:39:44-30-12-97 08:39:44 DeliveredDate: 30-12-97 08:39:44 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 C125657D.002A2109; Tue, 30 Dec 1997 08:42:06 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA27666; Tue, 30 Dec 1997 08:42:36 +0100 Date: Tue, 30 Dec 1997 08:42:36 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA27650 Received: (qmail 13304 invoked from network); 29 Dec 1997 23:42:34 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Dec 1997 23:42:34 -0800 Message-Id: <34A8ADFC.3376@dnvr.uswest.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu