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arXiv · 2212.10597

On the representation-free formalism in quantum mechanics

V. D. Efros
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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.

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V. D. Efros. 2022-12-20. On the representation-free formalism in quantum mechanics. https://doi.org/10.1007/s12648-025-03792-w

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