Operator method for calculating Q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols

We propose a new method for calculating Husimi symbols of operators. In contrast to the standard method, it does not require using the anti-normal-ordering procedure. According to this method, the coordinate and momentum operators $$\hat q$$ and $$\hat p$$ are assigned other operators $$\hat X$$ and $$\hat P$$ satisfying the same commutation relations. We then find the result of acting with the $$\hat X$$ and $$\hat P$$ operators and also polynomials in these operators on the Husimi function. After the obtained expression is integrated over the phase space coordinates, the integrand becomes a Husimi function times the symbol of the operator chosen to act on that function. We explicitly evaluate the Husimi symbols for operators that are powers of $$\hat X$$ or $$\hat P$$.