su(1,1) coherent states and a normal extension of su(1,1) annihilation operator: squeezed states and the simultaneous measurement of Q^{-1}P+PQ^{-1} and Q^{-2}

摘要

The the over-complete eigenvector system of the operator Q^{-1}P (Q:position,P:momentum) which consists of the squeezed states |0; s, t > with various s andt are investigated from the viewpoint of the annihilation and creationrelations related to the algebra su(1,1). We derive a positive operator-valuedmeasure(POVM) for the simultaneous measurement between the self-adjoint andanti-self-adjoint parts of PQ^{-1}.