Abstract
Based on the theory of deformed Lie algebra, we construct a nonlinear spectrum-generating algebra for the first P?schl-Teller potential by use of the Hamiltonian and the natural operators. This nonlinear algebra can determine the energy spectrum and the complete set of eigenfunctions, and can be converted into the harmonic oscillator algebra through a nonlinear transformation, which shows there is a new symmetry in the system.
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