WKB Approximation for Quaternionic Quantum Mechanics with Purely Imaginary Potentials

Solving the Schrödinger equation in quaternionic quantum mechanics (QQM) has been a nut to crack. In complex quantum mechanics (CQM), approximation methods has been used to find the solutions of the Schrödinger equation whem exact solutions are difficult to obatin. The present study challenges the earlier eikonal (or WKB) approximation formalism [17] developed for an imaginary quaternion potential. In this paper, the correct form of coupled equations, obeying the non-commutative structure, and approximated solution for quaternionic time-independent Schrödinger equation (QTISE) have been obtained.