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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:(Quasi-) exactly solvable `Discrete' quantum mecha
nics - Odake\, S (Shinshu)
DTSTART;TZID=Europe/London:20090323T113000
DTEND;TZID=Europe/London:20090323T123000
UID:TALK17536AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/17536
DESCRIPTION:This talk is based on the collaboration with Ryu S
asaki.\n`Discrete' quantum mechanics is a quantum
mechanical system whose Schr"{o}dinger equation is
a difference equation instead of differential in
ordinary quantum mechanics.\nWe present a simple r
ecipe to construct exactly and quasi-exactly solva
ble Hamiltonians in one-dimensional `discrete' qua
ntum mechanics.\nIt reproduces all the known ones
whose eigenfunctions consist of the Askey scheme o
f hypergeometric orthogonal polynomials of a conti
nuous or a discrete variable.\nAn essential role i
s played by the sinusoidal coordinate\, which gene
rates the closure relation and the Askey-Wilson al
gebra together with the Hamiltonian.\nWe also pres
ent the Crum's Theorem for `discrete' quantum mech
anics.
LOCATION:Seminar Room 1 Newton Institute
CONTACT:Mustapha Amrani
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