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Algebraic Methods in Ordinary Quantum Mechanics Revisited
Author(s) -
Ghirardi Gian Carlo
Publication year - 1973
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19730211202
Subject(s) - algebraic number , scheme (mathematics) , algebra over a field , mathematics , supersymmetric quantum mechanics , dimension of an algebraic variety , quantum , pure mathematics , quantum statistical mechanics , quantum mechanics , physics , mathematical analysis
We reconsider the problem of giving an algebraic treatment to quantum problems within the framework of ordinary quantum mechanics. After a concise review of the irreducible representations of the relevant Lie algebra, we formulate the general scheme within which all previous approaches can be easily fitted. We then show which are the explicit connexions between this general scheme and the specific approaches found in the literature. The whole paper constitutes a concise and synthetic summary of algebraic techniques in ordinary quantum mechanics.