Uncertainty Relation in Quantum Mechanics with Quantum Group(13)

We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the underlying noncom

UsingEqs.1-4one ndsthematrixelements:

xjr1,...,rn,s1,...,sn=Lj( [sj]qδrj+1,sj)·

(70)

(71)

(72)qr1+...+rj 1δr1,s1·...·δrj 1,sj 1δrj+1,sj+1·...·δrn,snTheeigenvalueproblemxjvλ=λvλisthensolvedbyallvλ=∞ sj=0fs1,...,sj,...,sn(λ)es1,...,en

withcoe cientsthatobeytherecursionformula(allsiarekept xedexceptsj):

L q (r1+...+rj 1)fs1,...,sj,...,sn(λ)