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)