Planar Rotor in Matrix Mechanics and the Role of States in Quantum Physics

TL;DR

This paper demonstrates how to analyze the planar quantum rotor using matrix mechanics without relying on eigenstates, and explores the fundamental role of states in quantum theory.

Contribution

It introduces a state-free approach to quantum spectra and discusses the conceptual implications for the role of states in quantum mechanics.

Findings

Spectrum obtained without eigenstates

Insights into the role of states in quantum mechanics

Speculation on eliminating states from quantum theory

Abstract

We illustrate Heisenberg's method of matrix mechanics using the planar quantum rotor example. We show how to find the spectrum of this simple model without the need to use the eigenstates of the system. This then leads us to speculate on the role the Heisenberg state plays in quantum mechanics and to ask whether one could even completely dispose of the need for states.