The Gravity and The Quantum: A Bohr-inspired Synthesis

An effective angular momentum quantization condition of the form $mvr=n\hbar(m/m_F)$ is used to obtain a Bohr-like model of Hydrogen-type atoms and a modified Schr\"{o}dinger equation. Newton's constant, $G$, of Gravitation gets explicitly involved through the fundamental mass $m_F$ as defined in the sequel. This non-relativistic formalism may be looked upon as a ``testing ground'' for the more general synthesis of the gravity and the quantum.