Hi i have the WKB approx of:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]u_{+} = \sqrt{1-\frac{bm}{f}}e^{i\int f_{k} dt} + \sqrt{1+\frac{bm}{f}}e^{-i\int f_{k} dt}[/itex]

to the differential equation:

[itex]\frac{d^{2}u_{+}}{dt^2} + [f_{k}^{2} + i(\frac{d(bm)}{dt})]u_{+} =0[/itex]

This equation can be written as:

[itex]\frac{d^{2}u_{+}}{dN^2} + [p^2 - i + M^2]u_{+} =0[/itex]

by using [itex]p=\frac{k}{\sqrt{\frac{\partial x}{\partial t}Cb_{*}(t_{*1})}}[/itex] and [itex]M=\sqrt{\frac{\partial x}{\partial t}Cb_{*}(t_{*1})}(t-t_{*})^{2}[/itex]

How to i find the asymptotic solutions for when [itex]M\rightarrow \pm ∞ [/itex] do i need to sub in using: [itex]f^{2}_{k}=k^2 + b^2(t_{*1})(\frac{\partial x}{\partial t}|_{*1})^2 (t-t_{*})^2 [/itex] and the above and then take the limit for M, i am a bit confused though because the broken down solutions :

[itex] \sqrt{1+\frac{bm}{f}}\rightarrow \sqrt{2} [/itex]

[itex]\sqrt{1-\frac{bm}{f}}\rightarrow \frac{p}{-\sqrt{2}M} [/itex]

[itex]e^{+i\int f_{k}dt}\rightarrow (\frac{p}{-2M})^{\frac{ip}{2}}e^{-\frac{iM^2}{2}}e^{\frac{-ip^2}{4}}\pm [/itex]

contain M but surely that is [itex]M\rightarrow \pm ∞ [/itex] so why is it there?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Asymptotic analysis to the WKB approx

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**