Department of Mathematics2024-11-1020030264-938110.1088/0264-9381/20/1/3122-s2.0-0037275542http://dx.doi.org/10.1088/0264-9381/20/1/312https://hdl.handle.net/20.500.14288/17156We use the theory of pseudo-Hermitian operators to address the problem of the construction and classification of positive-definite invariant inner-products on the space of solutions of a Klein-Gordon-type evolution equation. This involves dealing with the peculiarities of formulating a unitary quantum dynamics in a Hilbert space with a time-dependent inner product. We apply our general results to obtain possible Hilbert space structures on the solution space of the equation of motion for a classical simple harmonic oscillator, a free Klein-Gordon equation and the Wheeler-DeWitt equation for the FRW-massive-real-scalar-field models.AstronomyAstrophysicsQuantum science and technologyPhysicsParticles and field physicsJournal Article1361-6382180628200015Q15518