14. Derivation of the Schrödinger equation from classical physics.

14.1. Introducción. ....................................................................................................... 93
14.2 Schrödinger Equation. 94 ......................................................................................... 94
        Particle at rest. 94 ...................................................................................................... 94
        Particle with Coulomb Potential 95 ......................................................................... 95
14.3 Conclusions. 96 ......................................................................................................... 96


In this section, the Schrödinger equation is deduced in a very simple manner. The starting point is the assumption that the Universe and particles are formed by four-dimensional Planck atoms. The wave function is the ratio between the kinetic energy that the electron has when it is unobserved and the energy that it acquires due the observation

14.1. Introduction                                        Download Paper

In 1923, De Broglie suggested that all matter should behave as waves with a wavelength given by l/mv, where l is the wavelength of the particle, h is Planck's constant, m is the mass of the particle and v its velocity.
Motivated by the hypothesis of De Broglie, in 1926 Erwin Schrödinger conceived an equation as a way to describe the wave behaviour of particles of matter. The equation was later called the Schrödinger equation.
On the one hand, despite much debate, it is accepted that the square of the wave function at a point represents the probability density at that point. Max Born gave the wave function a different probabilistic interpretation than that given by De Broglie and Schrödinger, an interpretation that Einstein never shared.
On the other hand, Schrödinger published two attempts to derive the equation that takes his name[42,43]. There have also been attempts by other authors to obtain Schrödinger’s equation from different principles[44–50].
We can consider the electron as a Planck particle that is in the state of minimum energy. The Planck particle turns into angular velocity (ωe), dragging adjacent space atoms to a distance equal to half its wavelength.
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14.3 Conclusions

     The definition of the wave function as the ratio of the kinetic energy that has the electron and the energy that acquire when it’s been disturbed  as a result of the observation, give the wave function a physical meaning. This energy should check the Heisenberg uncertainty principle at all times
When we try to measure the precise position of the electron, the electron changes its energy, and, therefore, we vary its position. This position is recovered quickly, by issuing the energy absorbed.
The wave function has nothing to do with the probability of finding an electron in a given region of space. This function is the ratio of the unobserved electron energy and is acquired due to observation.

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