An attempt to construct quantum mechanics from Newton equations

We present one scheme for quantizing classical theories starting from their equations of motion. The procedure is such that the well-established quantum-mechanical results for conservative systems are recovered by construction. The method provides a unique way of quantizing classical systems irrespective of the nonexistence (or multiplicity) of Lagrangians for their equations of motion. We exhibit the quantization of the one-dimensional damped harmonic oscillator following this scheme.