Abstract

We develop Dirac's representation theory in quantum mechanics by constructing the nonlinear entangled state | η〉 nl and its non-Hermite conjugate state nl《η| with continuum variable. By virtue of the technique of integration within an ordered product of operators we show that | η〉 nl and nl《η| make up an orthonormal and complete representation. From | η〉 nl we also deduce another kind of entangled states. Application of | η〉 nl in studying two-mode squeezed state is demonstrated.

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