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WKB approximation

For $\epsilon^2y_{XX}+k^2(X)y=0$ with nonzero slowly varying $k$,
$$
y\sim k(X)^{-1/2}\left[
C_+e^{i\epsilon^{-1}\int^Xk(s)ds}
+C_-e^{-i\epsilon^{-1}\int^Xk(s)ds}
\right].
$$
It fails near turning points and where $\epsilon|k'|/|k|^2$ is not small.


WKB approximation for a slowly varying oscillator

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 336 / 3 / a / Solution

WKB approximation for a slowly varying oscillator

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WKB approximation for a slowly varying oscillator

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