부산대학교 도서관

\follows from CnoFile {1 612 279}{remarks} Summary of the first paper: ``Operators conjugate to the Hamiltonian are constructed explicitly for the quantum harmonic oscillator by two approaches in the space spanned by the eigenstates of $q$ and the eigenstates of $p$. The operators are quantum analogues of a classical angle variable divided by the oscillator frequency. Matrix elements are evaluated in the coherent state representation. Either conjugate operator can be used to construct an explicitly time-dependent operator invariant. It can be used as the starting point in a new perturbative procedure for constructing invariant operators for nonlinear, nonautonomous Hamiltonians.'' \par \{The comment by Smith and Vaccaro questions parts of the authors' arguments. They raise questions in regard to certain matrix elements of commutators and the use of the, in general multivalued, logarithm and arctangent functions in constructing the phase and time operators. The authors reply, defending their particular use of commutators and similarly the propriety of the use of the logarithm and arctangent in their particular context.\} \par \{For related, and in some respects more general, work see papers by C. M. Bender\ and G. V. Dunne\ [Phys. Rev. D (3) {\bf 40} (1989), no.~8, 2739--2742; MR1019516 (90m:81013); Phys. Rev. D (3) {\bf 40} (1989), no.~10, 3504--3511; MR1024743 (90k:81029)] and Bender [in {\it Lie algebras, cohomology, and new applications to quantum mechanics (Springfield, MO, 1992)}, 31--45, Contemp. Math., 160, Amer. Math. Soc., Providence, RI, 1994; MR1277373 (95e:81030)].\}