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

  • Authors:

  • Miloslav Znojil

  • Affiliations:

  • Nuclear Physics Institute ASCR, Řež, Czech Republic

  • Venue:
  • CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
  • Year:
  • 2011

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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.