Biquaternionic Description of the Schrödinger Equation

[摘要] This paper begins with the introduction of biquaternion algebra and its properties in compact, profound and comprehensible approach. The Schrödinger equation including both the scalar Aharonov-Bohm(sAB) and Aharonov-Casher(AC) effects, that are currently popular in particle physics and condensed-matter physics, has been re-written by biquaternions. The newly biquaternionic Schrödinger equation, which is defined with various assumptions and approaches, also includes the biquaternionic generalized momentum in Hamiltonian.

[学科分类] 计算数学

[关键词] Quaternion;Biquaternion;Schrödinger equation;Scalar Aharonov-Bohm (sAB) effect;Aharonov-Casher(AC) effect