Journal of Algebra, Number Theory: Advances and ApplicationsAuthor's: Ying-Qiu Gu
Pages: [17] - [34]
Received Date: March 13, 2020; Revised April 13, 2020.
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100122123
By constructing the commutative operators chain, we derive the integrable conditions for solving the eigenfunctions of Dirac equation and Schrödinger equation. These commutative relations correspond to the intrinsic symmetry of the physical system, which are equivalent to the original partial differential equation can be solved by separation of variables. Detailed calculation shows that, only a few cases can be completely solved by separation of variables. In general cases, we have to solve the Dirac equation and the Schrödinger equation by effective perturbation or approximation methods, especially in the cases including nonlinear potential or self-interactive potentials.
eigenfunction, commutative relation, separation of variables, nonlinear Dirac equation, Abelian Lie algebra, Clifford algebra.
