About Quantum Mechanics without Hamiltonians

Abstract

An extension of Shr ö dinger’s quantization on the space ( x , p ) , where the Hamiltonian approach is needed, is made on the space ( x , v ) where the Hamiltonian approach is not needed at all. The purpose of this paper is to give a possible extension of the actual formulation of the Quantum Mechanics, and this is achieved through a function K ( x , v , t ) which takes the place of the Hamiltonian on the Shr ö dinger’s equation and has units of energy. This approach allows us to include the quantization of classical velocity depending problems (dissipative) and position depending mass variation problems. Some examples are given.