Exact solutions and ladder operators for a new anharmonic oscillator

In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schrödinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r→ir.