Spectral density calculation by using the Chebyshev expansion

A method to calculate the spectral density of any state vectors with respect to a set of eigenstates of a Hamiltonian is presented. A spectral density operator, whose expectation value on the state vector gives the spectral density, is evaluated indirectly by using the Chebyshev expansion method. A spectral transformation function is introduced to improve resolution at the low energy region, at the expense of the one at the higher region. The predissociation spectrum of CO+ is calculated to demonstrate the method.