Some invariant biorthogonal sets with an application to coherent states

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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.
Original languageEnglish
Pages (from-to)462-476
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume415
Publication statusPublished - 2014

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Quantum theory
Hilbert spaces
Coherent States
Invariant
Unitary Operator
Quantum Mechanics
Hilbert space

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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title = "Some invariant biorthogonal sets with an application to coherent states",
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.",
author = "Salvatore Triolo and Fabio Bagarello and Bagarello",
year = "2014",
language = "English",
volume = "415",
pages = "462--476",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
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AU - Bagarello, Fabio

AU - Bagarello, null

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N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/93350

UR - http://www.sciencedirect.com/science/article/pii/S0022247X1400105X

M3 - Article

VL - 415

SP - 462

EP - 476

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

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