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This short pedagogical write-up explaining the Miller-Good improvement of the WKB approximation. Applications are relevant to bound states and quantum tunneling.
De Gruyter Proceedings in Mathematics
PDF] Reflection and transmission resonances and accuracy of the
Wentzel–Kramers–Brillouin approximation for atmospheric waves, Journal of Fluid Mechanics
PDF) The Miller-Good version of the WKB approximation in quantum mechanics
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Winitzki - Derivation of WKB Approximation, PDF, Approximation
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PDF) The Miller-Good version of the WKB approximation in quantum mechanics
Quantum Mechanics
PDF] Introduction to Quantum Mechanics by Harald J W Müller-Kirsten eBook
Upper and lower bounds for tunneling splittings in a symmetric
Applications of WKB