Use of the Lorentz-operator in relativistic quantum mechanics to guarentee a single-energy root
The Lorentz-operator form of relativistic quantum mechanics, with relativistic wave equation i{h_bar}{partial_derivative}{psi}/{partial_derivative}t=(mc{sup 2}{gamma}+e{Phi}){psi}, is implemented to guarantee a single-energy root. The Lorentz factor as modified by Pauli's ansatz is given by {gamma}={radical}1+[{rvec {sigma}}{center_dot}(i{h_bar}{rvec {del}}+(e/c){rvec A})]{sup 2}/m{sup 2}c{sup 2}, such that the theory is appropriate for electrons. Magnetic fine structure in the Lorentz relativistic wave equation emerges on the use of an appropriate operator form of the Lienard-Wiechert four- potential ({Phi},{rvec A}) from electromagnetic theory. Although computationally more intensive the advantage of the theory is the elimination of the negative-root of the energy and an interpretation of the wave function based on a one-particle, positive definite probability density like that of nonrelativistic quantum mechanics.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE Office of Defense Programs (DP)
- DOE Contract Number:
- W-7405-Eng-48
- OSTI ID:
- 3846
- Report Number(s):
- UCRL-ID-132202; DP0102011; ON: DE00003846
- Country of Publication:
- United States
- Language:
- English
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