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