  Quantum Hamiltonians containing nonseparable products of non-commuting
operators, such as $\hat{\bf x}^m \hat{\bf p}^n$, are problematic for numerical
studies using split-operator techniques since such products cannot be
represented as a sum of separable terms, such as $T(\hat{\bf p}) + V(\hat{\bf
x})$. In the case of classical physics, Chin [Phys. Rev. E $\bf 80$, 037701
(2009)] developed a procedure to approximately represent nonseparable terms in
terms of separable ones. We extend Chin's idea to quantum systems. We
demonstrate our findings by numerically evolving the Wigner distribution of a
Kerr-type oscillator whose Hamiltonian contains the nonseparable term $\hat{\bf
x}^2 \hat{\bf p}^2 + \hat{\bf p}^2 \hat{\bf x}^2$. The general applicability of
Chin's approach to any Hamiltonian of polynomial form is proven.
