Modified de Broglie-Bohm quantum trajectories and some insights into the Born's probability axiom
Dr. Moncy John
St Thomas College, Kozhencherry.
There is a renewed interest in the foundational issues of quantum mechanics in recent times. The earliest among the interpretations of quantum mechanics is the pilot wave theory of de Broglie, which envisages quantum trajectories. This was an attempt to unify the principles of mechanics and optics, which he also presented in the 1927 Solvay conference. But it was not well-received at that time and was soon forgotten. Later, David Bohm rediscovered it and is now known as de Broglie-Bohm (dBB) theory. A modified version of dBB, which is closer to the classical Hamilton -Jacobi theory, is presented. It is shown that this MdBB approach has several important advantages over the conventional dBB theory. Also it is demonstrated that in MdBB, the Born's probability density can be obtained from the velocity field of particles in a complex plane. The extended probability density in the complex plane helps to interpret the classical limit of quantum mechanics as one in which particles are confined close to the real line.