Abstract
We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schrödinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schrödinger equation or the Schrödinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form.
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