A Quantum Mechanical Proof of the Fourier Inversion Formula
The translation of the observable, position and momentum, of a given particle in the real line, at a certain time t, from Classical Mechanics, into the operators, position and momentum, in Quantum Mechanics, gives us the inspiration to make a proof of the existence of the Fourier's Inverse Tran...
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2011
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oai:scielo:S0716-091720110003000102012-06-18A Quantum Mechanical Proof of the Fourier Inversion FormulaCastro,Nelson N. de ORojas,JacquelineMendoza,Ramon Fourier transform position operator momentum operator extension The translation of the observable, position and momentum, of a given particle in the real line, at a certain time t, from Classical Mechanics, into the operators, position and momentum, in Quantum Mechanics, gives us the inspiration to make a proof of the existence of the Fourier's Inverse Transform, using algebraic relations involving these operators (position and momentum), a few of Linear Algebra and Analysis, without resorting to the classical technics like Fubini's Theorem and Lebesgue's Dominated Convergence Theorem.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.30 n.3 20112011-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000300010en10.4067/S0716-09172011000300010 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Fourier transform position operator momentum operator extension |
| spellingShingle |
Fourier transform position operator momentum operator extension Castro,Nelson N. de O Rojas,Jacqueline Mendoza,Ramon A Quantum Mechanical Proof of the Fourier Inversion Formula |
| description |
The translation of the observable, position and momentum, of a given particle in the real line, at a certain time t, from Classical Mechanics, into the operators, position and momentum, in Quantum Mechanics, gives us the inspiration to make a proof of the existence of the Fourier's Inverse Transform, using algebraic relations involving these operators (position and momentum), a few of Linear Algebra and Analysis, without resorting to the classical technics like Fubini's Theorem and Lebesgue's Dominated Convergence Theorem. |
| author |
Castro,Nelson N. de O Rojas,Jacqueline Mendoza,Ramon |
| author_facet |
Castro,Nelson N. de O Rojas,Jacqueline Mendoza,Ramon |
| author_sort |
Castro,Nelson N. de O |
| title |
A Quantum Mechanical Proof of the Fourier Inversion Formula |
| title_short |
A Quantum Mechanical Proof of the Fourier Inversion Formula |
| title_full |
A Quantum Mechanical Proof of the Fourier Inversion Formula |
| title_fullStr |
A Quantum Mechanical Proof of the Fourier Inversion Formula |
| title_full_unstemmed |
A Quantum Mechanical Proof of the Fourier Inversion Formula |
| title_sort |
quantum mechanical proof of the fourier inversion formula |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2011 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000300010 |
| work_keys_str_mv |
AT castronelsonndeo aquantummechanicalproofofthefourierinversionformula AT rojasjacqueline aquantummechanicalproofofthefourierinversionformula AT mendozaramon aquantummechanicalproofofthefourierinversionformula AT castronelsonndeo quantummechanicalproofofthefourierinversionformula AT rojasjacqueline quantummechanicalproofofthefourierinversionformula AT mendozaramon quantummechanicalproofofthefourierinversionformula |
| _version_ |
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