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A procedure allowing to construct rigorously discrete as well as continuumdeterministic evolution equations from stochastic evolution equations isdeveloped using a Dirac's bra and ket notation. This procedure is an extensionof an approach previously used by the authors coined Discrete StochasticEvolution Equations. Definitions and examples of discretes as well as continuumone-dimensional lattices are developed in detail in order to show the basictools that allows to construct Schr\"odinger-like equations. Extension tod-dimensional lattices are studied in order to provide a wider exposition andthe one-dimensional cases are derived as special cases, as expected. Somevariants of the procedure allows to construct other evolution equations. Also,using a limiting procedure, it is possible to derive the Schr\"odingerequations from the Schr\"odinger like equations.

A class of stochastic and distributions-free quantum mechanics evolution equations: The Schr\"odinger-like equations