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Volume 15: Pages 11-40, 2002
Quantum Field Derivation of the Superluminal Schrödinger Equation and Deuteron Potential
E. J. Betinis
Department of Physics, Elmhurst College, Elmhurst, Illinois 60126 U.S.A.
The superluminal Schrödinger equation originally derived by the author [Phys. Essays 11, 311 (1998)] was based on the author's derivation of the superluminal form of kinetic energy [Phys. Essays 11, 81 (1998)], which did not become singular at the velocity of light. This form of the kinetic energy then increased indefinitely as the particle velocity increased indefinitely without a singularity at v = c. The superluminal Schrödinger equation was then found by writing the kinetic energy as an operator by use of the usual quantum‐mechanical operator formalism corresponding to the superluminal kinetic energy. In the present paper, it is demonstrated that one can construct Lagrangian and Hamiltonian densities that allow the re‐derivation of the author's superluminal Schrödinger equation by the quantum field theory approach. Although not explored in the present paper, the quantum field so constructed may yield further insights into the world of superluminal physics. The superluminal spherically symmetric Schrödinger equation was solved for the eigenfunctions and, by a method of successive approximations, the spherically symmetric superluminal potential was found for the deuteron. The iterative procedure developed would be broadly classified as the inverse boundary value problem for finding the potential for the S‐state. The iterations were carried out by use of the Laplace transform. The solution of the third‐order differential equation derived by the author for superluminal quantum mechanics displayed unique characteristics. The principal objective was to find the attractive deuteron potential with a repulsive “hard” core. It was found that the potential obtained by use of the superluminal Schrödinger equation for all practical purposes had converged after the fourth iteration. Moreover, the poten tials calculated by the superluminal approach were very similar to those found by the author in a previous paper [Phys. Essays 6, 341 (1993)] and resembled the subluminal potentials found by Reid [B.L. Cohen, Concepts of Nuclear Physics (McGraw‐Hill, New York, 1974), p. 59]. In view of the fact that approximations had to be made to solve the superluminal Schrödinger equation, the potential found by iteration was acceptable as it had the general characteristics of those found before. Considerable care had to be exercised in carrying out the calculations numerically by use of the quite extensive computer program written. Since the potential found from the superluminal approach was, in essence, a reasonable extension of the subluminal potentials, this finding supports the idea that the author's superluminal theories of previous works are also valid. In this paper, it is shown that the boson exchanged between nucleons to mediate the nuclear force has a radial velocity v > c. In another paper [Phys. Essays 9, 135 (1996)], the author also showed by use of the Heisenberg uncertainty principle that this boson also had a radial velocity greater than c. The implication of the results of this paper and the 1996 paper above is that particles moving at v > c in the nucleus may also move at v > c upon their release from the nucleus and, if this contention is experimentally verified, the implication that follows is that the velocity‐of‐light limitation should be lifted from other branches of physics.
Keywords: quantum field theory, superluminal Schrödinger equation, superluminal nuclear potentials, Laplace transform, successive approximations, numerical differentiation and integration, third‐order differential equation
Received: February 25, 2000; Published online: December 15, 2008