Operator Method in the Problem of Quantum Anharmonic Oscillator

Relativistic Generalizations of the Quantum Harmonic Oscillator

“…In Table II the complex resonance energies of the onedimensional AO are displayed and compared with the results obtained on the basis of the operator method [35]. The maximal absolute error of each value does not exceed ±1 on the last digits, in all of the tables.…”

A High-Precision Study of Anharmonic-Oscillator Spectra

“…Feranchuk et al [70,10] and Ferna ndez et al [71] also start with a rescaling transformation of the sort discussed in Section 2. They develop perturbation expansions, of both Rayleigh Schro dinger and Brillioun Wigner types.…”

“…Reasonable accuracy is obtained for low eigenvalues of the quartic oscillator for small values of *. Improvement is sought [71,10] by modifying the rescaling parameter from the variational value determined in Section 2. This optimal-scaling procedure is quite successful; accuracies of up to 15 figures are obtained for low-lying states of the quartic oscillator over a wide range of values of *.…”

A Convergent Renormalized Strong Coupling Perturbation Expansion for the Ground State Energy of the Quartic, Sextic, and Octic Anharmonic Oscillator

“…An overview of the work on anharmonic oscillators before 1980 was given by Killingbeck [37]. More recent references can be found in [23] or in [38]. In addition, the anharmonic oscillators are treated in many textbooks on quantum field theory and related topics (see for instance pp.…”