A novel algebraic approach for the Schrödinger equation in split quaternionic mechanics

Guo, Zhenwei; Jiang, Tongsong; Васильев, В. И.; Wang, Gang

doi:10.1016/j.aml.2022.108485

Cited by 7 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, X σ is a solution to (9). Conversely, suppose that the real matrix Equation ( 9) has a solution,…”

Section: Split Quaternion Matrix Equation X ⋆ + Cx D = Ementioning

confidence: 99%

“…The theory of a split quaternion matrix has been studied with a focus on various aspects, such as in the following research: Erdo gdu et al [8] explored the matrix exponential e A with a complex adjoint. Guo et al [9] solved the eigen-problems of i-Hermitian split quaternion matrices due to their important applications on the Schrödinger equation, which is the fundamental equation of quantum mechanics. Jiang et al [10] studied the right eigenvalues and eigenvectors of split quaternion matrices and derived explicit formulas.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solution to Several Split Quaternion Matrix Equations

Liu,

Shi,

Zhang

2024

Mathematics

View full text Add to dashboard Cite

Split quaternions have various applications in mathematics, computer graphics, robotics, physics, and so on. In this paper, two useful, real representations of a split quaternion matrix are proposed. Based on this, we derive their fundamental properties. Then, via the real representation method, we obtain the necessary and sufficient conditions for the existence of solutions to two split quaternion matrix equations. In addition, two experimental examples are provided to show their feasibility.

show abstract

“…Thus, X σ is a solution to (9). Conversely, suppose that the real matrix Equation ( 9) has a solution,…”

Section: Split Quaternion Matrix Equation X ⋆ + Cx D = Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solution to Several Split Quaternion Matrix Equations

Liu,

Shi,

Zhang

2024

Mathematics

View full text Add to dashboard Cite

show abstract

“…However, it seems that the discussion and study of the problem of generalized eigenvalues of split quaternion matrices is not limited to complex values. Similar to the eigenvalues of split quaternion matrices [18][19][20][21][22][23], they should theoretically contain other forms of equivalence classes of cases. To this end, we consider the following a common kind of split quaternion generalized eigenvalue problem based on the least squares perspective.…”

Section: Introductionmentioning

confidence: 99%

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

Jiang,

Wang,

Guo

et al. 2024

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

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.

show abstract

The (anti‐)η$$ \eta $$‐Hermitian solution to a novel system of matrix equations over the split quaternion algebra

Gao,

Wang,

Xie

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

In comparison to quaternions, split quaternions exhibit a more intricate algebraic structure, characterized by the presence of nontrivial zero factors. Furthermore, in various fields such as geometry and electromagnetism, split quaternions serve as more convenient research tools than quaternions. This paper aims to establish the necessary and sufficient conditions for the existence of (anti‐) ‐Hermitian solutions to a novel system of matrix equations formulated over split quaternions. We also provide the general expression of such solutions when the system is solvable, along with the least squares (anti‐) ‐Hermitian solution in the case of inconsistency. To illustrate the key findings of this paper, numerical examples are presented.

show abstract

A novel algebraic approach for the Schrödinger equation in split quaternionic mechanics

Cited by 7 publications

References 11 publications

Solution to Several Split Quaternion Matrix Equations

Solution to Several Split Quaternion Matrix Equations

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

The (anti‐)η$$ \eta $$‐Hermitian solution to a novel system of matrix equations over the split quaternion algebra

Contact Info

Product

Resources

About