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Published in:
2011 | OriginalPaper | Chapter
Symbolic-Manipulation Constructions of Hilbert-Space Metrics in Quantum Mechanics
Author : Miloslav Znojil
Published in: Computer Algebra in Scientific Computing
Publisher: Springer Berlin Heidelberg
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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.