Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics
We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat the repulsive oscillator (hyperbolic case) and the free parti...
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2011-01-01
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doaj-6990734e51cd47d9a83a4c136432b2552020-11-24T23:17:49ZengCTU Central LibraryActa Polytechnica1210-27091805-23632011-01-015141402Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex MechanicsV. V. KisilWe revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat the repulsive oscillator (hyperbolic case) and the free particle (the parabolic case). The respective hypercomplex numbers turn out to be handy on this occasion. This provides a further illustration to the Similarity and Correspondence Principle.https://ojs.cvut.cz/ojs/index.php/ap/article/view/1402Heisenberg groupKirillov’s method of orbitsgeometric quantisationquantum mechanicsclassical mechanicsPlanck constantdual numbersdouble numbershypercomplexjet spaceshyperbolic mechanicsinterferenceFock-Segal-Bargmann representatio |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
V. V. Kisil |
spellingShingle |
V. V. Kisil Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics Acta Polytechnica Heisenberg group Kirillov’s method of orbits geometric quantisation quantum mechanics classical mechanics Planck constant dual numbers double numbers hypercomplex jet spaces hyperbolic mechanics interference Fock-Segal-Bargmann representatio |
author_facet |
V. V. Kisil |
author_sort |
V. V. Kisil |
title |
Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics |
title_short |
Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics |
title_full |
Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics |
title_fullStr |
Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics |
title_full_unstemmed |
Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics |
title_sort |
erlangen programme at large 3.2 ladder operators in hypercomplex mechanics |
publisher |
CTU Central Library |
series |
Acta Polytechnica |
issn |
1210-2709 1805-2363 |
publishDate |
2011-01-01 |
description |
We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat the repulsive oscillator (hyperbolic case) and the free particle (the parabolic case). The respective hypercomplex numbers turn out to be handy on this occasion. This provides a further illustration to the Similarity and Correspondence Principle. |
topic |
Heisenberg group Kirillov’s method of orbits geometric quantisation quantum mechanics classical mechanics Planck constant dual numbers double numbers hypercomplex jet spaces hyperbolic mechanics interference Fock-Segal-Bargmann representatio |
url |
https://ojs.cvut.cz/ojs/index.php/ap/article/view/1402 |
work_keys_str_mv |
AT vvkisil erlangenprogrammeatlarge32ladderoperatorsinhypercomplexmechanics |
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1725583191397367808 |