Four possible definitions of the commutation relation [S, T] = 11 of two closable unbounded operators S, T are compared. The weak sense of this commutator is given in terms of the inner product of the Hilbert space H where the operators act. Some consequences on the existence of eigenvectors of two numberlike operators are derived and the partial O*-algebra generated by S, T is studied. Some applications are also considered.
Bagarello, F., Inoue, A., Trapani, C. (2011). Weak commutation relations of unbounded operators and applications. JOURNAL OF MATHEMATICAL PHYSICS, 52 [10.1063/1.3660682].
Weak commutation relations of unbounded operators and applications
BAGARELLO, Fabio;TRAPANI, Camillo
2011-01-01
Abstract
Four possible definitions of the commutation relation [S, T] = 11 of two closable unbounded operators S, T are compared. The weak sense of this commutator is given in terms of the inner product of the Hilbert space H where the operators act. Some consequences on the existence of eigenvectors of two numberlike operators are derived and the partial O*-algebra generated by S, T is studied. Some applications are also considered.
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