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

0435946 - ÚJF 2015 RIV DE eng C - Conference Paper (international conference)
Znojil, Miloslav
Symbolic-Manipulation Constructions of Hilbert-Space Metrics in Quantum Mechanics.
Lecture Notes in Computer Science. Vol. 6885. Berlin: Springer, 2011 - (Gerdt, V.; Koepf, W.; Mayr, E.; Vorozhtsov, E.), s. 348-357. ISBN 978-3-642-23567-2. ISSN 0302-9743.
[13th International Workshop on Computer Algebra in Scientific Computing. Kassel (DE), 05.09.2011-09.09.2011]
R&D Projects: GA ČR GAP203/11/1433; GA MŠMT LC06002
Institutional support: RVO:61389005
Keywords : Hilbert spaces * Hamiltonian * operator equation
Subject RIV: BE - Theoretical Physics

The recently formulated quantum-mechanics problem of the determination of the Hilbert-space metric Theta 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 Dieudonne's operator equation) and analysis of suitable Theta = Theta(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.
Permanent Link: http://hdl.handle.net/11104/0239801