The Quantum Formalism Revisited

• URL: http://arxiv.org/abs/2506.16480v3
• Date: Thu, 09 Oct 2025 15:37:27 GMT
• Title: The Quantum Formalism Revisited
• Authors: Hajo Leschke,
• Abstract summary: For the simple system of a point-like particle confined to a straight line, I compile, initially in a concise table, the structural elements of quantum mechanics.<n>Despite many similarities, there are the well-known fundamental differences, resulting from the algebraic non-commutativity in the quantal structure.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: For the simple system of a point-like particle confined to a straight line, I compile, initially in a concise table, the structural elements of quantum mechanics and contrast them with those of classical (statistical) mechanics. Despite many similarities, there are the well-known fundamental differences, resulting from the algebraic non-commutativity in the quantal structure. The latter was discovered by Werner Heisenberg (1901-1976) in June 1925 on the small island of Helgoland in the North Sea, as a consequence of understanding atomic spectral data within a matrix scheme consistent with energy conservation. I discuss the differences and exemplify their quantifications by the variance and entropic indeterminacy inequalities, by (pseudo-)classical bounds on quantum canonical partition functions, and by the correlation inequalities of John Bell (1928-1990) and others.

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