Volume 4, Issue 4, pages 235-246
A. I. Arbab [Show Biography]
Arbab Ibrahim studied physics at Khartoum University and high energy physics at the International Cenetr for Theoretical Physics (ICTP), Italy. He has taught physics at Khartoum University and Qassim University, and he is currently a Professor of Physics. He has been a visiting scholar at University of Illinois, Urbana-Champaign, Towson University, and Sultan Qaboos University. His work concentrates on the formulation of quantum mechanics and electromagnetism using Quaternions. He has publications in wide range of theoretical physics. He is an active reviewer for many international journals.
By expressing the Schrödinger wavefunction in the form ψ=Re^iS, where R and S are real functions, we have shown that the expectation value of S is conserved. The amplitude of the wave (R) is found to satisfy the Schrödinger equation while the phase (S) is related to the energy conservation. Besides the quantum potential that depends on R, we have obtained a phase potential that depends on the phase S derivative. The phase force is a dissipative force. The quantum potential may be attributed to the interaction between the two subfields S and R comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass mc² with an internal frequency of 2mc²/h, satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz R satisfies the Klein-Gordon equation, then S must satisfies the wave equation. Conversely, if R satisfies the wave equation, then S yields the Einstein relativistic energy momentum equation.