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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Format: | Article |
Language: | English |
Published: |
CTU Central Library
2011-01-01
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Series: | Acta Polytechnica |
Subjects: | |
Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/1402 |
Summary: | 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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ISSN: | 1210-2709 1805-2363 |