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Annals of Physics

The Schrödinger equation in helical coordinates

Theoretical Physics

Published Nov 1, 1974• 0 citations
Publisher
DOI
10.1016/0003-4916(74)90411-4

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EULER’S FORMULA IS THE KEY TO UNLOCKING THE SECRETS OF QUANTUM PHYSICS

Bichara Sahely

In this short note, the the key to unlocking the secrets of quantum physics will be elucidated by exploring the fundamentals of Schrodinger's wave mechanics approach to describing quantum phenomenon. We will show that de Broglie's wave-particle duality hypothesis which lies at the heart of Schrodinger's wave-function \psi produces a complex wave equation whose mathematical structure can be described by Euler's famous equation e^{i\theta}=cos(\theta)+isin(\theta) which basically describes a helical wave in 3D space. By comparing and contrasting the electromagnetic wave with that of a helical wave which Euler's equation represents, we may have discovered the geometric basis for spin and helicity and antimatter with negative energies that Dirac uncovered in his relativistic reformulation of Schrodinger's equation.

•Apr 1, 2012•0 citations
In this short note, the the key to unlocking the secrets of quantum physics will be elucidated by exploring the fundamentals of Schrodinger's wave mechanics approach to describing quantum phenomenon. We will show that de Broglie's wave-particle duality hypothesis which lies at the heart of Schrodinger's wave-function \psi produces a complex wave equation whose mathematical structure can be described by Euler's famous equation e^{i\theta}=cos(\theta)+isin(\theta) which basically describes a helical wave in 3D space. By comparing and contrasting the electromagnetic wave with that of a helical wave which Euler's equation represents, we may have discovered the geometric basis for spin and helicity and antimatter with negative energies that Dirac uncovered in his relativistic reformulation of Schrodinger's equation.