Energy eigenvalues of d-dimensional quartic anharmonic oscillator

Abstract

On the basis of a radial generalization of the JWKB quantization rule, which incorporates higher orders of the approximation, an explicit analytical formula is derived for the energy levels of the three-dimensional quartic anharmonic oscillator. The formula exhibits the scaling property of the exact eigenvalues, and is readily generalized to any dimension. Together with the Hellmann–Feynman theorem, it yields the values of the diagonal moments of r2k. The predicted energies and moments are in excellent agreement with known numerical results.