Phys10 - On the Reality of Complex Harmonic Oscillator from Heisenberg to Circle Theory

A spring and a pendulum are two forms of the harmonic oscillator. They are described by derived differential equations and their solutions exhibit an oscillatory form like a wave. This oscillation is in real space and is defined as a classical harmonic oscillator.

Quantum mechanics is a theory that tries to explain the microscopic world. This theory is based on postulates. One of these postulates is the Schrödinger equation. It is an expostulated deferential equation and its solution is called the wave function. The wave function has a form of a complex harmonic oscillation. This oscillation is in Hilbert (complex) space. Thus, the Schrödinger equation may be referred to as a complex harmonic oscillator.

Circles theory is an attempt to find a physical explanation for a complex harmonic oscillator, and out of the approach of quantum mechanics. Circles theory is based on Heisenberg’s concepts of “nature in itself” and “observed nature”. “Nature in itself” is the nature that stands beyond the “observed nature”. In spite of that, the circles theory is not a quantum mechanics theory, but its forms are similar to the relativistic quantum mechanics forms.