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Semina Ciências Sociais e Humanas

O operador evolução

Antonio Fernando Prado de Andrade

Published Nov 29, 1983• 0 citations
Publisher

Abstract

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.

DOI
10.5433/1679-0383.1983v4n14p414

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O operador evolução

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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;} Discussão do problema do átomo de hidrogênio sem levar em conta o spin das partículas interagentes, apresentando-se, posteriormente, uma solução no espaço de momentum. A nálise de uma conexão entre a equação radial para o potencial Coulombiano e a equação radial para o potencial tipo oscilador harmônico multidimensional.

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<meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dwindows-1252"> <meta name=3DGenerator content=3D"Microsoft Word 11"> <meta name=3DOriginator content=3D"Microsoft Word 11"> <link rel=3DFile-List href=3D"IC_89_367yatodo_archivos/filelist.xml"> RESUMEN <!--[if gte mso 9]> Un usuario de Microsoft Office satisfecho. Normal Un usuario de Microsoft Office satisfecho. 2 2 2004-06-23T15:40:00Z 2004-06-23T15:40:00Z 1 44 243 UCLA 2 1 286 11.6568 <![endif]--><!--[if gte mso 9]> 0 Clean Clean 21 false false false MicrosoftInternetExplorer4 <![endif]--><!--[if gte mso 9]> <![endif]--> <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} span.SpellE {mso-style-name:""; mso-spl-e:yes;} @page Section1 {size:612.0pt 792.0pt; margin:70.85pt 3.0cm 70.85pt 3.0cm; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> <!--[if gte mso 10]> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabla 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;} <![endif]--> RESUMEN The quantum-mechanical problem with a time-dependent potencial is solved by the path integral method. The solution is obtained by the application of the previously derived general formula for rheonomic homogeneous point transformation and reparametrization in the path integral.

•Jan 1, 1989•0 citations

Probability operator for non-equilibrium systems

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Quantum Dynamics

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Abstract For present purposes, the first thing to recall about quantum mechanics is that all dynamical quantities, instead of being functions of the location of a system in phase space as in classical mechanics, are now represented by operators in a Hilbert space of quantum states. In particular, the quantum analog of the classical phase space distribution function is the quantum mechanical density matrix. Since this is seldom discussed in introductory texts on either quantum mechanics or statistical mechanics, it may be helpful to summarize some of its basic properties.

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Ising model across planar lattices

Ranasinghe P.K.C. Malmini

Normal 0 false false false MicrosoftInternetExplorer4 st1\:*{behavior:url(#ieooui) } /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table 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;} The Ising model on a two dimensional lattice with pentagon tiling and greater number of next to neighbours interaction is equivalent to the Ising model on the centered square lattice with nearest and next to nearest neighbour non-crossing interactions. We obtain exact expressions on calculation of critical temperature with ferromagnetic and anti-ferromagnetic interactions. A direct anti-ferromagnetic bond of strength α L can give rise to the transition temperatures for appropriate α. We apply the star-triangle mapping transformation technique and decorating transform to Ising model. Keywords: Exact results, Ising model, square lattice, transformations. doi:10.4038/jnsfsr.v36i4.268 Journal of the National Science Foundation of Sri Lanka 36 (4) 303-305

Journal of the National Science Foundation of Sri Lanka•Dec 30, 2008•0 citations
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.
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;} Discussão do problema do átomo de hidrogênio sem levar em conta o spin das partículas interagentes, apresentando-se, posteriormente, uma solução no espaço de momentum. A nálise de uma conexão entre a equação radial para o potencial Coulombiano e a equação radial para o potencial tipo oscilador harmônico multidimensional.
<meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dwindows-1252"> <meta name=3DGenerator content=3D"Microsoft Word 11"> <meta name=3DOriginator content=3D"Microsoft Word 11"> <link rel=3DFile-List href=3D"IC_89_367yatodo_archivos/filelist.xml"> RESUMEN <!--[if gte mso 9]> Un usuario de Microsoft Office satisfecho. Normal Un usuario de Microsoft Office satisfecho. 2 2 2004-06-23T15:40:00Z 2004-06-23T15:40:00Z 1 44 243 UCLA 2 1 286 11.6568 <![endif]--><!--[if gte mso 9]> 0 Clean Clean 21 false false false MicrosoftInternetExplorer4 <![endif]--><!--[if gte mso 9]> <![endif]--> <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} span.SpellE {mso-style-name:""; mso-spl-e:yes;} @page Section1 {size:612.0pt 792.0pt; margin:70.85pt 3.0cm 70.85pt 3.0cm; mso-header-margin:35.4pt; mso-footer-margin:35.4pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> <!--[if gte mso 10]> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabla 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;} <![endif]--> RESUMEN The quantum-mechanical problem with a time-dependent potencial is solved by the path integral method. The solution is obtained by the application of the previously derived general formula for rheonomic homogeneous point transformation and reparametrization in the path integral.
Abstract For present purposes, the first thing to recall about quantum mechanics is that all dynamical quantities, instead of being functions of the location of a system in phase space as in classical mechanics, are now represented by operators in a Hilbert space of quantum states. In particular, the quantum analog of the classical phase space distribution function is the quantum mechanical density matrix. Since this is seldom discussed in introductory texts on either quantum mechanics or statistical mechanics, it may be helpful to summarize some of its basic properties.
Normal 0 false false false MicrosoftInternetExplorer4 st1\:*{behavior:url(#ieooui) } /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table 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;} The Ising model on a two dimensional lattice with pentagon tiling and greater number of next to neighbours interaction is equivalent to the Ising model on the centered square lattice with nearest and next to nearest neighbour non-crossing interactions. We obtain exact expressions on calculation of critical temperature with ferromagnetic and anti-ferromagnetic interactions. A direct anti-ferromagnetic bond of strength α L can give rise to the transition temperatures for appropriate α. We apply the star-triangle mapping transformation technique and decorating transform to Ising model. Keywords: Exact results, Ising model, square lattice, transformations. doi:10.4038/jnsfsr.v36i4.268 Journal of the National Science Foundation of Sri Lanka 36 (4) 303-305