The exact solution of the Schrodinger equation with a polynomially spatially varying mass

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00312865" target="_blank" >RIV/68407700:21230/17:00312865 - isvavai.cz</a>
Result on the web
<a href="http://aip.scitation.org/doi/full/10.1063/1.4993194" target="_blank" >http://aip.scitation.org/doi/full/10.1063/1.4993194</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4993194" target="_blank" >10.1063/1.4993194</a>

Result language
angličtina
Original language name
The exact solution of the Schrodinger equation with a polynomially spatially varying mass
Original language description
The Schrodinger equation with a position-dependent mass (SEPDM) is employed in many areas of quantum physics. Exact solutions for the SEPDM lie at the center of interest of the professional public because it helps us to understand the behavior of quantum particles in the cases in which their mass varies spatially. For this purpose, we used the mass function represented by a quartic polynomial and a quadratic potential function, which extends the current class of exact solutions of the SEPDM. The exact analytical solution of the problem is expressed as a linear combination of local Heun functions. Heun's equation contains many parameters, resulting in its general nature. We studied how limit changes in some of these parameters will affect the solution of the SEPDM. The obtained solutions are particularly suitable for the transfer matrix method and solutions of scattering problems; this is demonstrated by the calculation of bound states.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10303 - Particles and field physics

Project
<a href="/en/project/GA15-23079S" target="_blank" >GA15-23079S: Acoustic wave propagation through nonlocal dispersion zones</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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