M Tater and A V Turbiner 1993 J. Phys. A: Math. Gen. 26 697 doi:10.1088/0305-4470/26/3/027
M Tater and A V Turbiner
Show affiliationsAn extended analysis of eigenvalues and wavefunctions resulting from the Hill determinant method is carried out for the one-dimensional sextic anharmonic oscillator. It is shown that, in spite of a seemingly natural ansatz of the method, irrelevant wavefunctions may appear, leading to incorrect eigenvalues. The domain of applicability of the method is limited and its practical use demands a priori investigation before concrete calculations of spectral characteristics. Effective variational calculations based on adequate trial functions are performed and comparison of the results of both approaches is presented.
03.65.Ge Solutions of wave equations: bound states
02.10.De Algebraic structures and number theory
11C20 Matrices, determinants (See also 15A36)
65K10 Optimization and variational techniques (See also 49Mxx, 93B40)
81Qxx General mathematical topics and methods in quantum theory
Issue 3 (7 February 1993)
M Tater and A V Turbiner 1993 J. Phys. A: Math. Gen. 26 697
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