Class of potentials, the quasi-classical quantization of which may be more precise

The new class of potentials, where for the exact quasi-classical quantization may be achieved through certain modification of the quantization conditions, is considered. The list of the potentials, wherefore the new list of the potentials, the spectrum whereof is determined by the factorization method. The uniparametric family of the quantization conditions, including the WKB-supersymmetrical condition, as a particular case, is plotted. The new condition makes it possible to consider various modifications of the top-level approximation and limits of their application, and also develop new approximated methods of the spectra calculation