SIMULTANEOUS EIGENSTATES OF THE NUMBER-DIFFERENCE OPERATOR AND A BILINEAR INTERACTION HAMILTONIAN DERIVED BY SOLVING A COMPLEX DIFFERENTIAL EQUATION

As a continuum work of Bhaumik et al.3 who derived the common eigenvector of the number-difference operator Q≡(a†a-b†b) and pair-annihilation operator ab, we search for the simultaneous eigenvector of Q and (ab-a†b†) by setting up a complex differential equation in the bipartite entangled state representation. The differential equation is then solved in terms of the two-variable Hermite polynomials and the formal hypergeometric functions. The work is also an addendum to Ref. 5 in which the common eigenkets of Q and pair creators a†b† are discussed.

EINSTEIN–PODOLSKY–ROSEN ENTANGLED STATE REPRESENTATION FOR ANGULAR-MOMENTUM AND RADIUS ENTANGLEMENT

By comparison with the Einstein–Podolsky–Rosen coordinate-momentum entangled state, which is the common eigenvector of two particles' relative coordinate and total momentum, we construct a new quantum mechanical entangled state representation, namely, the entangled state representation of angular-momentum and radius. A concrete physical system which can embody the new quantum entanglement is analyzed.