WKB approximation: Difference between revisions

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Hence, when <math>E > V(x)</math>, the wavefunction can be chosen to be expressed as:<math display="block">\Psi(x') \approx C \frac{\cos{(\frac 1 \hbar \int |p(x)|\,dx} + \alpha) }{\sqrt{|p(x)| }} + D \frac{ \sin{(- \frac 1 \hbar \int |p(x)|\,dx} +\alpha)}{\sqrt{|p(x)| }} </math>and for <math>V(x) > E</math>,<math display="block">\Psi(x') \approx \frac{ C_{+} e^{+- \frac{i1}{\hbar} \int |p(x)|\,dx}}{\sqrt{|p(x)|}} + \frac{ C_{-} e^{-+ \frac{i1}{\hbar} \int |p(x)|\,dx} }{ \sqrt{|p(x)|} } . </math>The integration in this solution is computed between the classical turning point and the arbitrary position x'.

=== Validity of WKB solutions ===