1978/04/19 by K. Banerjee, Kalyan Banerjee, S. P. Bhatnagar +3
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics
paper · doi:10.1098/rspa.1978.0086
Abstract Accurate eigenvalues and eigenfunctions of the anharm onic oscillator (H = p2 + x2 + λx4, λ > 0) and the quartic oscillator (H = p2 + x4) are obtained in all regimes of the quantum num ber n and the anharm onicity constant λ. Transition moments of comparable accuracy are obtained for the quartic oscillator. The method, applicable quite generally for eigenvalue problems, is non-perturbative and involves the use of an appropriately scaled basis for the determ ination of each eigenvalue. The appropriate scaling formula for a given regime of (n, λ) is constructed from the oscillation properties of the eigenfunctions. More general anharm onic oscillators are also discussed.