Abstract
Exact error bounds to the Bohr - Sommerfeld quantization formula are derived without a priori assuming quantum numbers to be large. The assessments are expressed in terms of a single quantity, the error-control integral, which is determined by the potential U(x) in a unique fashion as a function of a particle's total energy. While taken over the real axis, the integral has the advantage of being suitable for analytical investigation. Exact sufficient conditions are established for the Bohr - Sommerfeld formula to be extendible to the range of lower quantum numbers.
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