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 \(\hat P\) .