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
3Uncertaintyrelation
Forsimplicitywe rstconsiderthe1dimensionalcasewhereEq.14
reads:
with[x,p]=ih¯+ih¯(q2 1) x24K2
K=h¯
2A2
α( p)2 2 h¯
)2+ p 2
4L2+( p
2
2 1+(q2 1) ( x)+ x 2
4K2
6(24) (30)