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Some invariant biorthogonal sets with an application to coherent states

Fabio BagarelloSalvatore Triolo

subject

Pure mathematicsApplied MathematicsHilbert spaceFOS: Physical sciencesMathematical Physics (math-ph)Biorthogonal setsInvariant (physics)Unitary statesymbols.namesakeSettore MAT/05 - Analisi MatematicaBiorthogonal systemsymbolsCoherent statesCoherent stateMathematical PhysicsAnalysisMathematics

description

We show how to construct, out of a certain basis invariant under the action of one or more unitary operators, a second biorthogonal set with similar properties. In particular, we discuss conditions for this new set to be also a basis of the Hilbert space, and we apply the procedure to coherent states. We conclude the paper considering a simple application of our construction to pseudo-hermitian quantum mechanics.

yearjournalcountryeditionlanguage
2014-01-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2014.01.071