Thank you for your replies. Also, I apologize for a mistake in my question where I wrote that Bi possesses a "well-defined" Fourier transform; I only saw that Wolfram Functions had a (rather complicated-looking) formula for \mathscr F[\operatorname{Bi}](z), but looking more closely, I see that...
Hi,
Note: I will be sloppy with constant factors in this post. Only the general structure of the equations matters.
Consider a particle in a linear potential,
\frac{\mathrm d^2}{\mathrm d x^2} \psi(x) + x \psi(x) - E \psi(x) = 0.
Mathematically, this is a second-order ODE, and there...