Representations of Quantum Mechanics

Richard Healey

Gábor Hofer‐Szabó

The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical representation of classical conditional probabilities is situated within the broader frame of noncommutative representations. To this goal, we adopt some parts of the quantum formalism and ask whether empirical data can constrain the rest of the representation to conform to quantum mechanics. We will show that as the set of empirical data grows, conventional elements in the representation gradually shrink and the noncommutative representations narrow down to the unique quantum mechanical representation.

Alfredo Iorio

We discuss the q deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in Quantum Mechanics. We show that the q-deformation parameter labels the Weyl systems in Quantum Mechanics and the unitarily inequivalent representations of the canonical commutation relations in Quantum Field Theory. The von Neumann theorem in Quantum Mechanics (QM) states that for systems with finite number of degrees of freedom the representations of the canonical commutation relations (ccr), also called the Weyl representations, are each other unitarily equivalent. In the limit of infinite number of degrees of freedom, namely in Quantum Field Theory

A S Tarnovskiĭ

Roger G. Newton

Fan Hong-Yi, Lou Sen‐Yue, Xiao‐Yin Pan +1 more

In the previous studies and literatures, quantum mechanics representations are a pure state representation, while in this paper beginning with reasonable ordering of operators in quantum mechanics and the normal distribution thought in probability statistics, we propose the concept of quantum mechanics mixed state representation firstly,and prove its completeness and orthogonality. The advantages of mixed state representation is that it can reflect a variety of expression of quantum mechanics operators and the corresponding operators ordering rules.