Symbolic-manipulation constructions of Hilbert-space metrics in quantum mechanics

Abstract

The recently formulated quantum-mechanics problem of the determination of the Hilbert-space metric Θ which renders a given Hamiltonian H self-adjoint is addressed. Via an exactly solvable example of the so called Gegenbauerian quantum-lattice oscillator it is demonstrated that the construction (basically, the solution of the so called Dieudonné's operator equation) and analysis of suitable Θ = Θ(H) (i.e., the determination of their domain's "exceptional-point" boundary) may enormously be facilitated via symbolic algebraic manipulations and via the MAPLE-supported numerics and graphics. © 2011 Springer-Verlag.