Preprint: H. A. Yamani and Z Mouayn 12-2024

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Zouhair Mouayn

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Dec 6, 2024, 1:21:13 PM12/6/24

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Dear All,

Comments about Preprint are welcome.
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Best regards
Zouhair Mouayn
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Generalized coherent states for the harmonic oscillator by the J-matrix method with an extension to the Morse potential
Hashim A. Yamani, Zouhaïr Mouayn
While dealing with the J-Matrix method for the harmonic oscillator to write down its tridiagonal matrix representation in an orthonormal basis of L2(R); we rederive a set of generalized coherent states (GCS) of Perelomov type labeled by points z of the complex plane and depending on a positive integer number m The number states expansion of these GCS gives rise to coefficients that are complex Hermite polynomials whose linear superpositions provide eigenfunctions for the two-dimensional magnetic Laplacian associated with the mth Landau level. We extend this procedure to the Morse oscillator by constructing a new set of GCS of Glauber type.

2412.02958v2.pdf

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