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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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 47; no. 7; pp. 6205 - 6215
Main Authors: Jiang, Tongsong, Wang, Gang, Guo, Zhenwei, Zhang, Dong
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 15.05.2024
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9916