Abstract
A transform between the state space of one-dimensional quantum mechanical systems and a direct sum of two spaces of square integrable functions analytic on the open upper half-plane is constructed. It gives a representation of usual quantum mechanics on which the free evolution is trivial and the representation of canonical transformation very simple. Generalizations to higher dimensions are also discussed.
Keywords
MathematicsSquare-integrable functionTransformation (genetics)Integrable systemQuantumPlane (geometry)Analytic functionRepresentation (politics)Canonical transformationMathematical analysisQuantum mechanicsSimple (philosophy)Method of quantum characteristicsQuantum stateAnalytic continuationQuantum statistical mechanicsMathematical physicsClassical mechanicsPhysicsQuantum dynamicsQuantum operationGeometry
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Publication Info
- Year
- 1984
- Type
- article
- Volume
- 25
- Issue
- 11
- Pages
- 3252-3263
- Citations
- 72
- Access
- Closed
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Cite This
Thierry Paul
(1984).
Functions analytic on the half-plane as quantum mechanical states.
Journal of Mathematical Physics
, 25
(11)
, 3252-3263.
https://doi.org/10.1063/1.526072
Identifiers
- DOI
- 10.1063/1.526072