Is the Schrödinger Equation True?

Doug Jensen

Olavo Leopoldino da Silva Filho, Marcello Caio Ramon e Barros Ferreira

This is the fourth paper of a series devoted to mathematically derive the Schrödinger equation using stochastic constructs. We then show that Quantum Mechanics has a stochastic support by following two paths: we first present a stochastic derivation already known in the literature and show that it is equivalent to the characteristic function derivation, made by us in the first paper of this series. However, this approach does not furnish the true stochastic dynamics of the quantum mechanical system, but only an averaged one. We then present a new derivation of the Schrödinger equation based on Langevin equations that present all features of a true stochastic system. These two approaches then improve our understanding of Quantum Mechanics to encompass stochastic behavior.

Zbigniew Haba

We show that for a wide class of analytic potentials the solution of the Schrodinger equation can be expressed by the Wiener integral. We express the Feynman kernel by the Brownian bridge. We prove an asymptotic semiclassical expansion of the solution of the Schrodinger equation as well as of the Feynman kernel. We show that for a small time the van Vleck formula holds true as the limit h(cross) to 0 of the Feynman kernel.

акустика Механика

Mohamed Ashraf Farouk

Copenhagen physicists said; The electronics that we use today-radio, televisions, computers, lasers, MRI machines GPS-communications- depend on calculations using Schrodinger’s equation plus a lot of other Mathematics and Measurements, our idea of “shut up and calculate” has worked very well for us technologically. My comment’s these technological achievements do not justify that the equation itself as (I will try show) has any true scientific basis. In 1925, Erwin Schrodinger wrote excitingly to Einstein. “I have been intensely concerned these days with Louis de Broglie’s theory [1]. It is extraordinary, exciting, but still has some very grave difficulties”. So regardless of you are consider Schrodinger’s equation is a fundamental equation (has no derivation from simples forms) or derived one, you cannot deny first that Schrodinger’s equation is a wave equation and second it is shows how (de Broglie hypothesis of) matter wave change with time. i.e. Schrodinger equation describe the evaluation of the physical system in which the quantum effects, the “Wave-particle” duality are significant.