Symmetrized quartic polynomial oscillators and their partial exact solvability

0459199 - ÚJF 2017 RIV NL eng J - Článek v odborném periodiku
Znojil, Miloslav
Symmetrized quartic polynomial oscillators and their partial exact solvability.
Physics Letters. A. Roč. 380, č. 16 (2016), s. 1414-1418. ISSN 0375-9601. E-ISSN 1873-2429
Grant CEP: GA ČR GA16-22945S
Institucionální podpora: RVO:61389005
Klíčová slova: Quantum bound states * Non-numerical methods * Piecewise analytic potentials * Quartic oscillators * Quasi-extact states
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 1.772, rok: 2016

Sextic polynomial oscillator is probably the best known quantum system which is partially exactly alias quasi-exactly solvable (QES), i.e., which possesses closed-form, elementary-function bound states psi(x) at certain couplings and energies. In contrast, the apparently simpler and phenomenologically more important quartic polynomial oscillator is not QES. A resolution of the paradox is proposed: The one-dimensional Schrodinger equation is shown QES after the analyticity-violating symmetrization V(x)= A vertical bar x vertical bar + Bx(2) C vertical bar x vertical bar(3) + x(4) of the quartic polynomial potential.
Trvalý link: http://hdl.handle.net/11104/0259434