The time-dependent Schroedinger equation, Riccati equation and Airy functions

Nathan Lanfear, Sergei K. Suslov

We construct the Green functions (or Feynman's propagators) for the Schroedinger equations of the form $i{\psi }_t+1/4{\psi }_{xx}\pm t{x}^2\psi =0$ in terms of Airy functions and solve the Ca…