DETERMINATION OF THE COMMON EIGENVECTOR SYSTEM OF OPERATORS COMMUTING IN PAIRS

Shi-Min Xu, Xing-Lei Xu, Hongqi Li

Alejandro Medina

THIS WORK CONTAINSAN ANALYSIS OF SOME OF THE FUNDAMENTAL PRINCIPLES UNDERLAYING THE CONSTRUTION OF OPERATORS IN QUANTUM MECHANICS. FACH OPERATOR IS ASSOCIATED TO A PROJECTION OPERATOR AND THESE PROJECTION OPERATORS ARE SHOWS TO FULFIL A SET OF PROPERTIES FORMALLY INDENTICAL TO THOSE OF A PROBABILITY FIELD.IT IS SHOWN THAT, BY THE INTRODUCTION OFA MEASURE IN CONFIGURATION SPACE IT IS POSSIBLE TO OBTAIN COMPLETE SETS OF COMMUTING OBSERVABLES HAVING, WITHIN LIMITS, PREASIGNED SPECTRA. THE INTRODUCTION OF NEW OPERATORS BY CONSIDERATION OF THE GROUPS EXPRESSING THE SYMMETRIES OF THE SYSTEM, IS DISCUSSED.

А. А. Зайцев

Fan Hong‐Yi, John R. Klauder

Some comments are presented on the equivalence between Dirac’s ξ-representation of a harmonic oscillator (Ref. 5) and the eigenvectors of a creation operator derived by Fan et al. using Heitler’s contour integration form of δ-function. On the basis of this analysis the common eigenvectors of a†b† and Q=a†a−b†b, which are dual vectors of the charged coherent states of Bhaumik et al., are constructed.

LI Hong-cai, 福建师范大学物理系

The Hermitian cosine and sine operators for two particular models of two-mode space are obtained. As they commute, the common eigenstates are constructed. The properties of the operators and eigenvectors are discussed. The expectation values of these operators under the P-B phase representation are also studied.