Use of the Lorentz-operator in relativistic quantum mechanics to guarentee a single-energy root

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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 ... continued below

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Ritchie, A B August 1, 1998.

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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.

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  • Other: DE00003846
  • Report No.: UCRL-ID-132202
  • Grant Number: W-7405-Eng-48
  • DOI: 10.2172/3846 | External Link
  • Office of Scientific & Technical Information Report Number: 3846
  • Archival Resource Key: ark:/67531/metadc682610

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  • August 1, 1998

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  • July 25, 2015, 2:20 a.m.

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  • May 6, 2016, 11:09 p.m.

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Ritchie, A B. Use of the Lorentz-operator in relativistic quantum mechanics to guarentee a single-energy root, report, August 1, 1998; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc682610/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.