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Open Quantum Systems Decoherence
Entanglement Theory Quantum Correlations
Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states
arXiv
Authors: K. Thirulogasanthar, S. Twareque Ali
Year
2012
Paper ID
8567
Status
Preprint
Abstract Read
~2 min
Abstract Words
55
Citations
N/A
Abstract
We define quaternionic Hermite polynomials by analogy with two families of complex Hermite polynomials. As in the complex case, these polynomials consatitute orthogonal families of vectors in ambient quaternionic L2-spaces. Using these polynomials, we then define regular and anti-regular subspaces of these L2-spaces, the associated reproducing kernels and the ensuing quaternionic coherent states.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We define quaternionic Hermite polynomials by analogy with two families of complex Hermite polynomials.
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