Conformal Einstein PP-Wave as Quantum Solutions

We study conformal geometry on two essential classes of pp-wave spaces, i.e., Cahen-Wallach and two-symmetric spaces. This study leads to the general description of conformally Einstein metrics on the spaces under consideration. Having settled a model for the potential energy of the capacitor, we prove that the multiplying functions of conformal Einstein pp-wave spaces are solutions to the Schrödinger equation.