Application of nonstandard analysis to quantum mechanics
- 1 February 1975
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 16 (2), 177-200
- https://doi.org/10.1063/1.522525
Abstract
Quantum mechanics is formulated using a nonstandard Hilbert space. The concept of an eigen vector of a linear operator, which applies to standard as well as nonstandard Hilbert spaces, is replaced by the more general concept of an ultra eigen vector, which applies to nonstandard Hilbert spaces alone. Ultra eigen vectors corresponding to all spectral points of internal self−adjoint operators are proved to exist. This result enables us to set up a formalism which is equally valid for the discrete, as well as the continuous spectrum. Finally, Dirac’s formalism is reproduced, in a rigorous form within the nonstandard Hilbert space structure.Keywords
This publication has 2 references indexed in Scilit:
- The nonstandard λ:φ24(x): model. I. The technique of nonstandard analysis in theoretical physicsJournal of Mathematical Physics, 1972
- Dirac Formalism and Symmetry Problems in Quantum Mechanics. I. General Dirac FormalismJournal of Mathematical Physics, 1969