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- W2763465312 abstract "This chapter deals with the WKB(J) approximation, commonly used in applied mathematics and mathematical physics to find approximate solutions of linear ordinary differential equations (of any order in principle) with spatially varying coefficients. The WKB(J) approximation is closely related to the semiclassical approach in quantum mechanics in which the wavefunction is characterized by a slowly varying amplitude and/or phase. The chapter first introduces an inhomogeneous differential equation, from which the first derivative term is eliminated, before discussing the Liouville transformation and the one-dimensional Schrödinger equation. It then presents a physical interpretation of the WKB(J) approximation and its application to a potential well. It also considers the “patching region” in which the Airy function solution (the local turning point) is valid, the relation between Airy functions and Bessel functions, Airy integral and related topics, and related integrals." @default.
- W2763465312 created "2017-10-20" @default.
- W2763465312 creator A5058429193 @default.
- W2763465312 date "2017-05-30" @default.
- W2763465312 modified "2023-09-27" @default.
- W2763465312 title "Introduction to the WKB(J) Approximation: All Things Airy" @default.
- W2763465312 doi "https://doi.org/10.23943/princeton/9780691148373.003.0007" @default.
- W2763465312 hasPublicationYear "2017" @default.
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