Algebraic algorithms for a class of Schrödinger equations in split quaternionic mechanics

With the breakthroughs made by physicists in high‐dimensional mathematics, it has become possible to represent and solve a number of classical mathematical physics problems using the split quaternion algebra. In this paper, we study the least squares approximation of a class of Schrödinger equations...

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Vydané v:Mathematical methods in the applied sciences Ročník 47; číslo 7; s. 6205 - 6215
Hlavní autori: Jiang, Tongsong, Wang, Gang, Guo, Zhenwei, Zhang, Dong
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Freiburg Wiley Subscription Services, Inc 15.05.2024
Predmet:
Algorithms
complex representation matrix
generalized eigen‐problem
Mechanics (physics)
Quaternions
real representation matrix
Schrodinger equation
split quaternion matrix
split quaternionic mechanics
ISSN:0170-4214, 1099-1476
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Popis
Shrnutí:With the breakthroughs made by physicists in high‐dimensional mathematics, it has become possible to represent and solve a number of classical mathematical physics problems using the split quaternion algebra. In this paper, we study the least squares approximation of a class of Schrödinger equations in split quaternionic mechanics and propose two algebraic algorithms to the generalized right eigen‐problem for an i‐Hermitian split quaternion matrix pencil by using two isomorphic mappings. Numerical examples show the effectiveness of the proposed theories and algorithms.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9916