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.
Bagarello, F., Triolo S (2014). Some invariant biorthogonal sets with an application to coherent states. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 415(Issue 1), 462-476 [10.1016/j.jmaa.2014.01.071].
Some invariant biorthogonal sets with an application to coherent states
BAGARELLO, Fabio;TRIOLO, Salvatore
2014-01-01
Abstract
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.
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