The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics

We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein-Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the gen...

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Published inCommunications in theoretical physics Vol. 61; no. 6; pp. 683 - 685
Main Author 刘丽彦 郝清海
Format Journal Article
LanguageEnglish
Published 01.06.2014
Subjects
Coulomb potential
Dirac equation
Dirac方程
Mathematical analysis
Quantum mechanics
Scalars
Theoretical physics
Two dimensional
Vectors (mathematics)
一般形式
向量
库仑势
标量势
相对论量子力学
精确可解势
调和势
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ISSN0253-6102
1572-9494
DOI10.1088/0253-6102/61/6/04

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Summary:We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein-Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.
Bibliography:quasi-exactly solvable, Dirac equation, Klein-Gordon equation, scalar and vector potentials
We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein-Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.
11-2592/O3
LIU Li-Yan, HAO Qing-Hai（ College of Science, Civil Aviation University of China, Tianjin 300300, China）
ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/61/6/04