Probability distribution of αa+2 + \̄gaa−2 + βa+a− + γa−a+

Let {a+, a−, I} be generators of Heisenberg algebra with one degree of freedom. The general self-adjoint homogeneous quadratic function of {a+, a−} is αa+2 + \̄gaa−2 + βa+a− + γa−a+, which may be interpreted as the Hamiltonian of a certain quantum mechanical system. The probability distribution of this observable in any coherent state is calculated by means of Wick symbol calculus. In particular, the probability law of the observable 12 PQ + + QP), which is the Jordan product of the position observable Q = a+ + a− and the momentum observable P = i(a+ − a−), is obtained.