Uncertainty Relation in Quantum Mechanics with Quantum Group(9)

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

3.2Generalisationtondimensions

Letusnowreturntothendimensionalcasewherewewillrecoveressentiallythesamebehaviour:

ItisstraightforwardtoseethatthederivationofEq.30alsoworksinthendi-mensionalcasei.e.weget:

x1j pj≥

2| [xj,pj] |

andsolving,inordertoobtaine.g. xjmin:

2+1+1

q2 qq2 q2

2 s 1 x2s

4Ks2

+(q2 1) q2+1

4L2+ pj 2

j(48)