Symmetrized quartic polynomial oscillators and their partial exact solvability
Result description
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.
Keywords
Quantum bound statesNon-numerical methodsPiecewise analytic potentialsQuartic oscillatorsQuasi-extact states
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Symmetrized quartic polynomial oscillators and their partial exact solvability
Original language description
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.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
—
Result continuities
Project
GA16-22945S: Quantum Wheeler-DeWitt equation and its unitary evolution interpretation
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Physics Letters. A
ISSN
0375-9601
e-ISSN
—
Volume of the periodical
380
Issue of the periodical within the volume
16
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
5
Pages from-to
1414-1418
UT code for WoS article
000373537600004
EID of the result in the Scopus database
2-s2.0-84959211200
Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2016