The operator is expressed as an expansion in Chebyshev polynomials
In order to use the Chebyshev polynomials, the range of eigenvalues of the operator has to be adjusted by the substitution
The summation of the derived vectors is continued until the deviation of the coefficients from zero drops below a given accuracy. This makes it possible to achieve any desired accuracy up to computer accuracy.
The Chebyshev method is preferentially used for propagation of time-independent operators for otherwise it has to be run several times for subintervals of time over which it is assumed to be constant. The same has to be done if intermediate states in time are sought. Both will reduce the efficiency of the method.