Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics

Authors

  • V. V. Kisil

DOI:

https://doi.org/10.14311/1402

Keywords:

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

Abstract

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.

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Author Biography

  • V. V. Kisil

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Published

2011-01-04

Issue

Vol. 51 No. 4 (2011)

Section

Articles

How to Cite

Kisil, V. V. (2011). Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics. Acta Polytechnica, 51(4). https://doi.org/10.14311/1402