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## Main Question or Discussion Point

I am trying to solve the following differential equation:

[tex]

(\frac{L^2}{6k^2}+\frac{w\sqrt{3}}{2}\sin^2\theta\cos 2\phi)\psi=E\psi

[/tex]

where [tex]L^2 [/tex]is the angular momentum given by:

[tex] \frac{1}{\sin\theta}\frac{\partial}{\partial\theta}(sin\theta\frac{partial}{\partial\theta})-\frac{1]{sin^2\theta}\frac{\partial^2}{\partial\phi^2}

[/tex]. [tex] \theta [/tex] goes from 0 to [tex] \pi [/tex] while [tex] \phi [/tex] goes from 0 to 2 [tex] \pi [/tex]. [tex] k [/tex] and [tex] w[/tex] are constants and E is the energy of the system.. This differential equation seems non separable. Any ideas how to solve it...I also realised that the term [tex] sin^2\theta\cos 2\phi [/tex] is a combination of [tex] (Y_{2,-2]+ Y_{2,2}) [/tex]. But then how to continue?

Thanks

[tex]

(\frac{L^2}{6k^2}+\frac{w\sqrt{3}}{2}\sin^2\theta\cos 2\phi)\psi=E\psi

[/tex]

where [tex]L^2 [/tex]is the angular momentum given by:

[tex] \frac{1}{\sin\theta}\frac{\partial}{\partial\theta}(sin\theta\frac{partial}{\partial\theta})-\frac{1]{sin^2\theta}\frac{\partial^2}{\partial\phi^2}

[/tex]. [tex] \theta [/tex] goes from 0 to [tex] \pi [/tex] while [tex] \phi [/tex] goes from 0 to 2 [tex] \pi [/tex]. [tex] k [/tex] and [tex] w[/tex] are constants and E is the energy of the system.. This differential equation seems non separable. Any ideas how to solve it...I also realised that the term [tex] sin^2\theta\cos 2\phi [/tex] is a combination of [tex] (Y_{2,-2]+ Y_{2,2}) [/tex]. But then how to continue?

Thanks