A new version of the Hill-determinant construction of bound states is proposed. It is based on the matching of two suitable power-series Ansätze for the wave function. For the asymmetric well potential V(x)=ax+bx2+cx3+dx4 the convergence of the approximants to the physical solutions is proved. For b≳bminimal, the Taylor coefficients for this anharmonic oscillator’s wave function are specified by four-term recurrences.
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Miloslav Znojil (1992) studied this question.
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