Normal product form of two-mode Wigner operator

In the context of normal product, we use the method of the integration within an ordered product (IWOP) of operators to derive three representations of the two-mode Wigner operator: SU (2) symmetric description, SU (1, 1) symmetric description and polar coordinate form. We find that two-mode Wigner operator has multiple potential degrees of freedom. As the physical meaning of the selected integral variable changes, Wigner operator shows different symmetries. In particular, in the case of polar coordinates, we reveal the natural connection between the two-mode Wigner operator and the entangled state representation.

Quantum entangling or disentangling by complex integration transformation

We find some new integration transformations in complex space, which plays the role of entangling or disentangling in quantum mechanics. Their applications in operator ordering are presented. We employ the entangled state representation and the method of integration within ordered product of operators (IWOP) to find them.

Solving Schrödinger equation for bipartite hard-core potential by virtue of the entangled state representation

We study the one-dimensional Schrödinger equation for the Hamiltonian involving the bipartite hard-core potential, [Formula: see text]. We select the suitable unitary transformation and employ the entangled state representation |η⟩, η = η1 + iη2, to find the quantization condition for energy E, [Formula: see text] which seems new.