Consider E>V(x). WKB states the wavefunction will remain sinusoidal with a slow variation of wavelength $ \lambda $ and amplitude given that V(x) varies slowly. From the equation \begin{equation}(adsbygoogle = window.adsbygoogle || []).push({});

k(x)=\frac{\sqrt{2m(E-V(x))}}{\hbar}

\end{equation}, I can see that the k(x) is directly proportional to E-V(x), implying that $ \lambda $ is inversely proportional to E-V(x). I cannot understand why the amplitude should change with a variation in V(x). I do know that if E-V(x) becomes negative then the wavefunction becomes exponentially decaying in which case the wavefunction is no longer a periodic function (hence, amplitudes and wavelengths no longer apply). What is the equation connecting amplitude with V(x)? I am stuck and unable to proceed any further. Sorry about the equation numbering. I am rather new to LATEX

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# WKB Approximation

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