Symbolic-Manipulation Constructions of Hilbert-Space Metrics in Quantum Mechanics

  • Miloslav Znojil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)


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.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Miloslav Znojil
    • 1
  1. 1.Nuclear Physics Institute ASCRŘežCzech Republic

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