부산대학교 도서관

Summary of the first paper: ``Operators conjugate to the Hamiltonian are constructedexplicitly for the quantum harmonic oscillator by two approaches inthe space spanned by the eigenstates of $q$ and the eigenstates of$p$. The operators are quantum analogues of a classical angle variabledivided by the oscillator frequency. Matrix elements areevaluated in the coherent state representation. Either conjugateoperator can be used to construct an explicitly time-dependentoperator invariant. It can be used as the starting point in a newperturbative procedure for constructing invariant operators fornonlinear, nonautonomous Hamiltonians.''\par\{The comment by Smith and Vaccaro questions parts of the authors'arguments. They raise questions in regard tocertain matrix elements of commutators and the use ofthe, in general multivalued, logarithm and arctangent functions inconstructing the phase and time operators. The authors reply, defendingtheir particular use of commutators and similarly the propriety of theuse of the logarithm and arctangent in their particular context.\}\par\{For related, and in some respects more general, work see papers byC. 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)].\}