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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10303 - Particles and field physics

Projekt

<a href="/cs/project/GA15-23079S" target="_blank" >GA15-23079S: Šíření akustických vln nelokálními disperzními zónami</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

1089-7658

Svazek periodika

58

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

—

Kód UT WoS článku

000406764000022

EID výsledku v databázi Scopus

2-s2.0-85024493603