Applying quantum mechanics to macroscopic and mesoscopic systems

TL;DR

This paper proposes a framework where quantum mechanics can describe macroscopic and mesoscopic systems by introducing a system-dependent quantum of action, $h_{o}$, which is larger than Planck's constant.

Contribution

It introduces a new quantum of action, $h_{o}$, enabling quantum formalism application to larger-scale systems beyond microscopic particles.

Findings

Quantum of action $h_{o}$ is system-dependent and larger than Planck's constant.

Quantum mechanics formalism can be extended to macroscopic systems using $h_{o}$.

The action $S$ is quantized as integer multiples of $h_{o}$.

Abstract

There exists a paradigm in which Quantum Mechanics is an exclusively developed theory to explain phenomena on a microscopic scale. As the Planck's constant is extremely small, $h\sim10^{-34}{J.s}$, and as in the relation of de Broglie the wavelength is inversely proportional to the momentum; for a mesoscopic or macroscopic object the Broglie wavelength is very small, and consequently the undulatory behavior of this object is undetectable. In this paper we show that with a particle oscillating around its classical trajectory, the action is an integer multiple of a quantum of action, $S = nh_{o}$. The quantum of action, $h_{o}$, which plays a role equivalent to Planck's constant, is a free parameter that must be determined and depends on the physical system considered. For a mesoscopic and macroscopic system: $h_{o}\gg h$, this allows us to describe these systems with the formalism of quantum mechanics.