Quantum mechanics and linearized gravitational waves

The interaction of classical gravitational waves (GW's) with matter is studied within a quantum mechanical framework. The classical equations of motion in the long wavelength limit are quantized and a Schr\"odinger equation for the interaction of GW's with matter is proposed. Because of quadrupole nature, the GW interacts with matter by producing squeezed quantum states. The resultant Hamiltonian is quite different from what one would expect from general principles, however. The interaction of GW's with the free particle, the harmonic oscillator, and the hydrogen atom is then studied using this Hamiltonian.