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Instances of discrete quantum systems coupled to a continuum of oscillatorsare ubiquitous in physics. Often the continua are approximated by a discreteset of modes. We derive analytical error bounds on expectation values of systemobservables that have been time evolved under such discretised Hamiltonians.These bounds take on the form of a function of time and the number of discretemodes, where the discrete modes are chosen according to Gauss quadrature rules.The derivation makes use of tools from the field of Lieb-Robinson bounds andthe theory of orthonormal polynominals.

Dynamical error bounds for continuum discretisation via Gauss quadrature rules, -- a Lieb-Robinson bound approach