https://doi.org/10.1140/epjp/s13360-023-03819-3
Regular Article
Exponential unitary integrators for nonseparable quantum Hamiltonians
1
Department of Physics, Astronomy and Mathematics, University of Hertfordshire, AL10 9AB, Hatfield, UK
2
Tulane University, LA 70118, New Orleans, USA
Received:
18
November
2022
Accepted:
16
February
2023
Published online:
13
March
2023
Quantum Hamiltonians containing nonseparable products of non-commuting operators, such as 
, are problematic for numerical studies using split-operator techniques since such products cannot be represented as a sum of separable terms, such as 
. In the case of classical physics, Chin [Phys. Rev. E 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 
. The general applicability of Chin’s approach to any Hamiltonian of polynomial form is proven.
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