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Semina Ciências Biológicas e da Saúde

O operador evolução

Antonio Fernando Prado de Andrade

Published Dec 15, 1983• 0 citations
Publisher

Abstract

In this work we intend to develop the Mathematical Formalism of Non-Relativistic Quantum Mechanics in terms of two Basics Operators: Evolution Operator, and Density Operator and some of its properties. This article has didactic purposes.
DOI
10.5433/1679-0367.1983v4n14p414

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O operador evolução

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Normal 0 21 false false false MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabela normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} In this work we intend to develop the Mathematical Formalism of Non-Relativistic Quantum Mechanics in terms of two Basics Operators: Evolution Operator, and Density Operator and some of its properties. This article has didactic purposes.

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Normal 0 21 false false false MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabela normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} In this work we intend to develop the Mathematical Formalism of Non-Relativistic Quantum Mechanics in terms of two Basics Operators: Evolution Operator, and Density Operator and some of its properties. This article has didactic purposes.
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The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schreodinger's equation for the density matrix is fist obtained and from it Schroedinger's equation for the wave functions is derived. The momentum and position operators acting upon the density matrix are defined and it is then demonstrated that they commute. Pauli's equation for the density matrix is also obtained. A statistical potential formally identical to the quantum potential of Bohm's hidden variable theory is introduced, and this quantum potential is reinterpreted through the formalism here proposed. It is shown that, for dispersion free {\it ensembles% }, Schroedinger's equation for the density matrix is equivalent to Newton's equations. A general non-ambiguous procedure for the construction of operators which act upon the density matrix is presented. It is also shown how these operators can be reduced to those which act upon the wave functions.