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The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr–Sommerfeld quantization condition, revisited
The semiclassical limit, as the Planck constant $\hbar$ tends to $0$, of bound states of a quantum particle in a one-dimensional potential well is considered. The semiclassical asymptotic formulas for eigenfunctions are justified, and the BohrâSommerfeld quantization condition is recovered.