Feed: Dr. Myron Evans
Posted on: Monday, November 22, 2010 11:08 PM
Author: metric345
Subject: Reduction of the Dirac to Schroedinger Equations
| The clearest method is based on the reduction of the relativistic momentum gamma m v to the non relativistic limit, p = mv. The Dirac equation is essentially the quantization of the relativistic momentum in the format of the Einstein energy equation E = T + E0, where T is the relativistic kinetic energy and where E0 is the rest energy. The Einstein energy equation is another algebriac format of the relativistic momentum. Here E is known as the total relativistic energy. The Schroedinger equation H psi = E psi is obtained from the expression for non relativistic kinetic energy, T = p squared / (2m). The operators to be used for quantization are found from p sup mu = i h bar partial sup mu. Here p sup mu is (E / c, p), i.e. is defined by the total relativistic energy E and relativistic momentum p. To find the Dirac equation the d’Alembertian is expressed in terms of the metric and Dirac matrices. However, in UFT 129 and UFT 130 I developed the Dirac equation using only 2 x 2 matrices, another basic discovery of the development of ECE theory. The relativistic momentum emerged from the conservation of momentum in special relativity (J. B. Marion and S. T. Thornton, “Classical Dynamics”, third edition, pp. 525 ff.) If re expressed, the relativistic momentum becomes the Einstein energy equation. If the relativistic force is derived from the relativistic momentum, the relativistic kinetic energy is the work integral eq. (14.55) , page 527 of Marion and Thornton. The total energy is E = gamma m c squared, the relativistic kinetic energy is T = (gamma – 1) m c squared. In the limit v << c, T reduces to p squared / (2 m), and the Schroedinger equation is the quantization of this. It is very important to bear these basic definitions in mind. Both Dirac and Schroedinger come from gamma m v, but in different ways.
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