Werner Heisenberg, Louis de Broglie and Erwin Schrödinger revisited

Resumen o Introducción

The author argues that, for consistency, the de Broglie wavelength of a moving material particle should take account of the medium in which the particle is moving. Louis de Broglie posited that a moving material particle should be considered in the same way as a photon. Now, the wavelength of a photon is related to the medium in which it propagates and it seems only logical that, for a moving material particle the nature of the medium should be captured by the inclusion of something which characterizes that medium. It is shown that this 'something' is the index of refraction.

The de Broglie wavelength is then shown to be given by: l = h/p.r , where h is Planck's constant, p, the momentum of the particle and r, the index of refraction. Further, it is demonstrated that the inclusion of the index of refraction in the de Broglie wavelength alters Heisenberg's position/momentum relationship (but not the energy/time relationship), and, in addition, modifies the Schrödinger equations. All of these return to their commonly recognized forms when the index of refraction is set equal to its vacuum value.