The Pöschl-Teller (PT) potential occupies a privileged place among the anharmonic oscillator potentials due to its applications from quantum mechanics to diatomic molecules. For this potential, a polynomial su(1, 1) algebra has been constructed previously. So far, the coherent states (CSs) associated with this algebra have never appeared. In this paper, we construct the coherent states of the Barut-Girardello coherent states (BG-CSs) type for the PT potentials, which have received less attention in the scientific literature. We obtain these CSs and demonstrate that they fulfil all conditions required by the coherent state. The Mandel parameter for the pure BG-CSs and Husimi's and P-quasi distributions (for the mixed-thermal states) is also presented. Finally, the exponential form of the BG-CSs for the PT potential has been presented and enabled us to build Perelomov type CSs for the PT potential. We point out that the BG-CSs and the Perelomov type coherent states (PCSs) are related via Laplace transform. C 2014 AIP Publishing LLC.
We construct so(3) algebra associated with the Morse potential and show that these operators obey so(3) commutation relations. A so(3) algebraic method is proposed in order to obtain the eigenvalues and eigenfunctions of the Morse potential. This method exhibits that Cartan operatorĴ z , the lowering operatorĴ − , and the raising operatorĴ + determine successfully energy eigenvalues, the lowest energy eigenfunction, and excited energy eigenfunctions, respectively. C 2013 AIP Publishing LLC.
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