Energy Eigenvalues of Quantum Anharmonic Oscillators: Exact Expression for the Pure λx2m Oscillators and a Simple Expression for x2 + λx2m Oscillators

Abstract

We propose an exact expression for the energy eigenvalues of the pure λx2m quantum anharmonic oscillators. The only information needed for the purpose is K0(m,n), which is the first term of strong-coupling expansion for oscillator with potential λx2m for the nth excited state. We then propose simple expression for the eigenvalues of the x2 + λx2m oscillators which reproduce both the ground state and excited states energies of these oscillators with a fairly good accuracy. The present formula is found to better reproduce the energy eigenvalues than those calculated by earlier authors.