On the representation-free formalism in quantum mechanics

TL;DR

This paper introduces a new representation-free formalism in quantum mechanics that overcomes the limitations of the bra-ket approach, enabling more flexible and practical calculations.

Contribution

A novel representation-free scheme in quantum mechanics that avoids bra-ket drawbacks and supports both one-space and dual-space interpretations.

Findings

The new scheme is free from bra-ket formalism drawbacks.

It supports both one-space and dual-space interpretations.

It is well-suited for practical representation-free calculations.

Abstract

The widespread bra-ket formalism offers valuable tools for conducting representation-free considerations in quantum theory. However, it is not without its drawbacks. In this work, we discuss these drawbacks in detail and subsequently construct a new representation-free scheme. Similar to the bra-ket formalism, the present scheme provides essential means to facilitate representation-free considerations. At the same time, it is entirely free from the drawbacks of the bra-ket formalism. Unlike the dual-space bra-ket formalism, the present scheme allows both one-space and dual-space interpretations, which is a beneficial feature. The constructed universal scheme is very well-suited for performing representation-free practical calculations.