Unitary operator

Russell ( [ 17 ] ) has showed that , a compact perturbation , generated from unitary operator groups in infinite-dimensional linear Hilbert spaces , is unable to make the perturbed semigroup exponentially stable .

Russell（[17]）曾指出，无限维Hilbert空间中的酉算子群对生成的紧扰动不能使被扰动半群具有指数稳定性。

Properties of κ - photon unitary operator

k光子么正算符的性质

As it is well known , in Hilbert space , the representation transformation is realized by the unitary operator , so it is more suitable to use the optical method for pattern recognition .

由于表象变换是通过么正变换实现的，用光学方法进行图形识别是比较合适的。

Coherent-entangled state is a relatively unique one which is of coherence and entanglement characteristics . Making the representation transformation to the coherent-entangled state , we have derived a new squeezing operator in a nature way and found this unitary operator can satisfy the group multiplication rule .

相干纠缠态是一类比较特殊的表象，皆有相干和纠缠的特性，从相干纠缠态表象下的表象变换出发，我们导出了一个新的压缩算符，并且发现该算符具有群乘的性质。

In this paper , the Parameter dependant formulation of the Bogoliubov transformation is used to diagonalize Hamiltonian of Heisenberg antiferromagnet two sublattice modle , and to derive the spin dependant unitary operator performing this transformation and the exact eigenstates .

利用参量相关的Bogoliubov变换公式对角化Heisenberg反铁磁双子晶格模型哈密顿，得到施行变换的自旋相关的幺正算符和精确本征态。

Five kinds of symmetry transformation operations and corresponding symmetry transformation operators in quantum mechanics are introduced and the proof of linearity and unitary of transformation operator as well as the deduction of its formula is also given .

介绍了量子力学中的五种对称变换操作及相应的对称变换算符，并给出了变换算符线性和幺正性的证明及其表示式的推导。

Coordinate exchange and unitary transformation of momentum operator

角动量算符的表象变换与坐标轮换