Reailizations of U-q(su(1,1)) by deformed quantum harmonic oscillator algebras and associated deformed heisenberg algebras

摘要

For su(1,1)-symmetric Hamiltonians of quantum mechanical systems (e.g. single-mode quantum harmonic oscillator, radial Schrodinger equation for Coulomb problem or isotropic quantum harmonic oscillator, etc.), the Heisenberg algebra of phase-space variables in two dimensions satisfy the bilienar commutation relation [ip,x]=1 (in normal units). Also there are different realizations of su(1,1) by the generators of quantum harmonic oscillator algebra. We seek here the forms of deformed Hieisenberg algebras (bilinear in deformed x and ip) associated with deforms su(1,1)-symmetric hamiltonians.