Re[2]: Re: Re: Quantum Algebra
- To: mathgroup at smc.vnet.net
- Subject: [mg41286] Re[2]: [mg41269] Re: [mg41259] Re: Quantum Algebra
- From: Stepan Yakovenko <yakovenko at ngs.ru>
- Date: Tue, 13 May 2003 04:18:40 -0400 (EDT)
- References: <200305100803.EAA25980@smc.vnet.net> <200305110749.DAA03062@smc.vnet.net> <69296045.20030511164001@ngs.ru> <3EBFC826.3020107@wolfram.com>
- Reply-to: Stepan Yakovenko <yakovenko at ngs.ru>
- Sender: owner-wri-mathgroup at wolfram.com
Hello David, Monday, May 12, 2003, 11:13:26 PM, you wrote: DT> Stepan Yakovenko wrote: >>Hello David, >>DT> Thank you for your explanation. I look forward to trying out your >>DT> notebook. By the way, when I studied quantum mechanics I remember >>DT> learning that there are essentially only two exactly solvable physical >>DT> quantum mechanical systems, namely the 3D harmonic oscillator and the >>DT> hydrogen atom (and possibly the square well, although that's not really >>DT> a physical system). For all the rest, various approximation techniques >>DT> need to be used. Can these systems still be solved algebraically? If so, >>DT> how? >> >>In fact they can. >>One can sum all the orders of the pertrubation theory and get >>the analytic result with complex infinite sums as coefficients. >> >> >> >> DT> Thank you. That's interesting - I didn't realize that. So are the DT> results represented as sums or closed-form expressions? Yes, see A.Messia's "Quantum Mechanics part 2". I've got it in Russian in PDF (I can send it to you if it'll help), the original is in French. I've used these techniques to model optical waveguides (in linear case, of course) (that's quite close to QM), and I'll possibly publish these results in a year or so. -- Best regards, Stepan mailto:yakovenko at ngs.ru
- References:
- Re: Quantum Algebra
- From: Cesar Guerra <guerra_cesar@yahoo.com>
- Re: Re: Quantum Algebra
- From: David Terr <dterr@wolfram.com>
- Re: Quantum Algebra