GENERALIZED SCHRODINGER REPRESENTATIONS .1.

The formalism of the generalized Schrödinger representation is described and related to the standard formulations of quantum mechanics. The characteristic feature of a generalized Schrödinger representation is the appearance in the formalism of operators corresponding to quasi-observables, which are dynamical variables which cannot be measured directly; the operator corresponding to a quasi-observable does not exist in the Hilbert-space formalism. The use of generalized Schrödinger representations allows one to exhibit a remarkably simple and beautiful correspondence which exists between the classical and quantum theories in a large class of problems. A detailed discussion of the application to the one-dimensional harmonic oscillator, to the one-coordinate angular momentum problem, to the two-coordinate angular momentum problem, to the free particle in three-dimensions, and to the three-dimensional harmonic oscillator is given. © 1969.