A Plastino^1,2*

¹Departamento de F´ısica, Universidad Nacional de La Plata, Argentina
²Argentina’s IFLP-CCT-Conicet-Consejo Nacional de Investigaciones Cient´ıficas y Tecnol´ogicas, Argentina

*Corresponding Author: A Plastino, Departamento de F´ısica, Universidad Nacional de La Plata, Argentina.

Received: January 10, 2023; Published: February 06, 2023

Abstract

We uncover which is the Hamiltonian that has a coherent state as its ground state. Thus, we explain here how coherent states (CS) become eigenfunctions of a displaced quadratic potential V (x) that depends on the CS amplitude α. For each amplitude we have a different V (x). The associated ground state is a coherent state.

Keywords: Coherent States; Exact Analytic Form; Potential Function

References

1. R J Glauber. “Photon Correlations”. Physical Review Letters 10 (1963): 84.
2. R J Glauber. “The Quantum Theory of Optical Coherence”. Physical Review 130 (1963): 2529.
3. R J Glauber. Physical Review 131 (1963): 493.
4. R J Glauber. “Quantum Optics and Electronics”. ed. C. deWitt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, (1965).
5. G L Ferri., et al. “New mathematics for the nonadditive Tsallis’ scenario”. International Journal of Modern Physics B 31 (2017): 1750151.
6. I S Gradshteyn and I M Ryzhik. “Table of Integrals, Series and Products”. 3.462,4, p.338. Press (1965).
7. A Plastino and M C Rocca. Revista Mexicana de Física 65 (2019): 191.
8. E Schroedinger. Naturwissenschaften 14 (1926): 664.
9. V V Dodonov and V I Manko. Theory of Nonclassical States of Light (Taylor and Francis, London) (2003).
10. GS Agarwal and K Tara. “Nonclassical properties of states generated by the excitations on a coherent state”. Physical Review A 43 (1991): 492.
11. A Dehghani., et al. “Asymptotic Bessel-function expansions for Legendre and Jacobi functions”. Journal of Mathematical Physics 60 (2019): 083501.

Citation

Citation: A Plastino. “Hamiltonians that Generate Coherent States as their Ground States". Acta Scientific Applied Physics 3.3 (2023): 22-24.

Copyright

Copyright: © 2023 A Plastino. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.