1997/10/06 by H. S. Sharatchandra, Sharatchandra, H. S.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9710020
10 pages. Revtex
arxiv created 1997/10/06 · arxiv updated 2009/12/01
Requirements of a conjugate operator are emphasized, especially in its role in uncertainty relations.It is argued that in many contexts it is necessary to extend the Hilbert space in order to define a conjugate operator as in gauge theories. Example of a particle in a box is analysed. This is closely related to the quantum oscillator through cosine states of Susskind and Glogower.It is used to justify London's phase wave functions albeit as part of a larger Hilbert space. A new definition phase uncertainty neccessiated by periodicity is proposed.It is close to the usual r.m.s. definition.Corresponding number- phase uncertainty relation is obtained and its implications are discussed. Hilbert space of an oscillator is identified with the Hilbert space of a planar rotor with a Z2 gauge invariance.This is used to construct states analogous to the cosine and sine states and to illustrate unitary equivalence of Hilbert spaces.