WKB equivalent potentials for q-deformed harmonic and anharmonic oscillators

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Abstract
WKB equivalent potentials (WKB‐EP’s) giving the same WKB spectrum as the q‐deformed harmonic oscillator are determined in analytic form. For q being complex the WKB‐EP resembles the Pöschl–Teller, Morse, or Woods–Saxon potentials, widely used in nuclear, hypernuclear, and molecular physics. For q real, the WKB‐EP still goes to infinity at large x, while at small x it resembles a sextic oscillator. The WKB‐EP’s of the anharmonic oscillators with Uq(2) or SUq(1,1) symmetries, used for the description of vibrational molecular spectra, are also calculated. They correspond to q‐deformed versions of the modified Pöschl–Teller potential.

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