Nonlinear entangled state representation in quantum mechanics

We develop Dirac''s representation theory in quantum mechanics by constructing the nonlinear entangled state <f>&z.sfnc;η〉nl</f> and its non-Hermite conjugate state <f>nl&z.ldang;η&z.sfnc;</f> with continuum variable. By virtue of the technique of integration within an ordered product of operators we show that <f>&z.sfnc;η〉nl</f> and <f>nl&z.ldang;η&z.sfnc;</f> make up an orthonormal and complete representation. From <f>&z.sfnc;η〉nl</f> we also deduce another kind of entangled states. Application of <f>&z.sfnc;η〉nl</f> in studying two-mode squeezed state is demonstrated. [Copyright &y& Elsevier]