Are there any techniques in guessing the ground state wave function in any given potential?
For example, for a given potential like $$ \frac{1}{1-x^2}$$ or $$ \frac{1}{1-x^3}~?$$ I know wave function is sine or cosine inside the well and outside would be like exponential growth or decay depends on which side. Could I find the turning point by equating kinetic energy, $$ \frac{1}{2} m x'^2 ~?$$
