I would like to solve for the following eigenvalue equation: $$ A\frac{d^2}{dx^2}f(x) + B(1-e^{-Cx})^2 f(x) = \mu f(x) $$ $A<0$, $B>0$, and $C>0$ are real, positive constants with $\mu$ being the eigenvalue. My text indicates that this equation can be solved exactly with eigenvalue of the form $$ \mu_n = \alpha \left(n+\frac{1}{2}\right) + \beta \left(n+\frac{1}{2}\right)^2 $$ where $\alpha$ and $\beta$ some constants. I would appreciate any help.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.