Energy spectra of the hyperbolic and second Pöschl–Teller like potentials solved by new exact quantization rule

A new exact quantization rule simplifies the calculation of the energy levels for the exactly solvable quantum system. In this work we calculate the energy levels of the Schrödinger equation with the hyperbolic potential by this quantization rule. The corresponding eigenfunction is also derived for completeness. The second Pöschl–Teller like potential case is also carried out.