Dynamical Mappings of Density Operators in Quantum Mechanics. II. Time Dependent Mappings
- 1 September 1962
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 3 (5) , 848-852
- https://doi.org/10.1063/1.1724298
Abstract
The most general continuous time‐dependent evolution of a physical system is represented by a continuous one‐parameter semi‐group of linear mappings of density operators to density operators. It is shown that if these dynamical mappings form a group they can be represented by a group of unitary operators on the Hilbert space of state vectors. This proof does not assume that the absolute values of inner products of state vectors or ``transition probabilities'' are preserved but deduces this fact from the requirement that density operators are mapped linearly to density operators. An example is given of a continuous one‐parameter semi‐group of dynamical mappings which is not a group.Keywords
This publication has 5 references indexed in Scilit:
- Dynamical Mappings of Density Operators in Quantum MechanicsJournal of Mathematical Physics, 1961
- On Unitary Ray Representations of Continuous GroupsAnnals of Mathematics, 1954
- Symmetric Operators in Hilbert SpaceProceedings of the London Mathematical Society, 1948
- One-Parameter Semigroups of Isometric Operators in Hilbert SpaceAnnals of Mathematics, 1947
- On Unitary Representations of the Inhomogeneous Lorentz GroupAnnals of Mathematics, 1939