For the cubic radial anharmonic oscillator, a three-parameter interpolating wavefunction gives energies accurate to roughly seven to eight digits and wavefunctions within about 1e-4 across all distances.
Let us find the asymptotic behavior of y(r) at small w, y = (2 Mℏm) 1 m+2 × ( ˜ε0 Dw + ˜ε2 0 D2 (D + 2)w3 − a2pδp,3/2 D + 3 w4 + 2˜ε3 0 −a2pD3(D + 2)δp,2 D3(D + 2)(D + 4) w5 +
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Radial Anharmonic Oscillator: Perturbation Theory, New Semiclassical Expansion, Approximating Eigenfunctions. I. Generalities, Cubic Anharmonicity Case
For the cubic radial anharmonic oscillator, a three-parameter interpolating wavefunction gives energies accurate to roughly seven to eight digits and wavefunctions within about 1e-4 across all distances.