In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f（λQ ＋ VP） in it...In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f（λQ ＋ VP） in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations.展开更多
The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such op...The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.展开更多
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2015AM025)the Natural Science Foundation of Heze University,China(Grant No.XY14PY02)
文摘In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f（λQ ＋ VP） in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations.
文摘The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.
