2024-03-29T08:18:58Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698982022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Ultra-Weak Time Operators of Schrodinger OperatorsArai, AsaoHiroshima, F.open accesscanonical commutation relations, time operator, ultra-weak time operator, Schr¨odinger operator.410In 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 Schr¨odinger operators HV 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 : R ! R such that f(HV ) has an ultra-weak time operator is found.Department of Mathematics, Hokkaido University2016-07-27engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84238http://hdl.handle.net/2115/6989810.14943/84238Hokkaido University Preprint Series in Mathematics1094137https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69898/1/pre1094.pdfapplication/pdf247.59 KB2016-07-27