# Quantum Harmonic Analysis of the Density Matrix

## TL;DR

This paper rigorously examines mixed quantum states, their density matrices, and explores the implications of varying Planck's constant, aiming to bridge mathematical physics and quantum physics perspectives.

## Contribution

It provides a rigorous mathematical analysis of density matrices and discusses quantum-mechanical effects of changing Planck's constant, with dual focus for physicists and mathematicians.

## Key findings

- Rigorous formulation of mixed states and density matrices
- Analysis of quantum effects of varying Planck's constant
- Bridging mathematical and physical perspectives

## Abstract

We will study rigorously the notion of mixed states and their density operators (or matrices.) We will also discuss the quantum-mechanical consequences of possible variations of Planck's constant h. This Review has been written having in mind two readerships: mathematical physicists and quantum physicists. The mathematical rigor is maximal, but the language and notation we use throughout should be familiar to physicists.