Quantum square-well with logarithmic central spike
Result description
Singular repulsive barrier V (x) = -g ln(vertical bar x vertical bar) inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction L-eff(x) = -g ln[psi* (x)psi(x)] in nonlinear Schrodinger equation. In the linearized case, Rayleigh-Schrodinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small g or after an amendment of the unperturbed Hamiltonian. At any spike strength g, the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables x - exp y which interchanges the roles of the asymptotic and central boundary conditions.
Keywords
state-dependence of interactionseffective Hamiltonianslogarithmic nonlinearitieslinearized quantum toy model
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
Quantum square-well with logarithmic central spike
Original language description
Singular repulsive barrier V (x) = -g ln(vertical bar x vertical bar) inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction L-eff(x) = -g ln[psi* (x)psi(x)] in nonlinear Schrodinger equation. In the linearized case, Rayleigh-Schrodinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small g or after an amendment of the unperturbed Hamiltonian. At any spike strength g, the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables x - exp y which interchanges the roles of the asymptotic and central boundary conditions.
Czech name
—
Czech description
—
Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Result continuities
Project
GA16-22945S: Quantum Wheeler-DeWitt equation and its unitary evolution interpretation
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Modern Physics Letters A
ISSN
0217-7323
e-ISSN
—
Volume of the periodical
33
Issue of the periodical within the volume
2
Country of publishing house
SG - SINGAPORE
Number of pages
13
Pages from-to
—
UT code for WoS article
000423033400002
EID of the result in the Scopus database
2-s2.0-85040829798
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Year of implementation
2018