# Ultra-Weak Time Operators of Schrödinger Operators

Ultra-Weak Time Operators of Schrödinger Operators In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schrödinger operators $${H_V}$$ H V with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions $$f:{\mathbb {R}}\rightarrow {\mathbb {R}}$$ f : R → R such that $$f({H_V})$$ f ( H V ) has an ultra-weak time operator is found. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales Henri Poincaré Springer Journals

# Ultra-Weak Time Operators of Schrödinger Operators

, Volume 18 (9) – May 24, 2017
39 pages

/lp/springer_journal/ultra-weak-time-operators-of-schr-dinger-operators-cFMsKuSqmn
Publisher
Springer Journals
Subject
Physics; Theoretical, Mathematical and Computational Physics; Dynamical Systems and Ergodic Theory; Quantum Physics; Mathematical Methods in Physics; Classical and Quantum Gravitation, Relativity Theory; Elementary Particles, Quantum Field Theory
ISSN
1424-0637
eISSN
1424-0661
D.O.I.
10.1007/s00023-017-0586-x
Publisher site
See Article on Publisher Site

### Abstract

In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schrödinger operators $${H_V}$$ H V with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions $$f:{\mathbb {R}}\rightarrow {\mathbb {R}}$$ f : R → R such that $$f({H_V})$$ f ( H V ) has an ultra-weak time operator is found.

### Journal

Annales Henri PoincaréSpringer Journals

Published: May 24, 2017

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