Seeley-DeWitt expansion of scattering phase shift

In this paper, we use the Seeley-DeWitt expansion of heat kernel method in quantum field theory to give an explicit expression of the perturbation expansion for the scattering phase shift for three-dimensional spherically symmetric potential scattering in quantum mechanics. The spectral function is defined by the eigenproblem of an operator, and the spectral functions are related by transforms. The heat kernel and the scattering phase shift are both spectral functions of the Hamiltonian. By a transform between the heat kernel and the scattering phase shift, we convert the Seeley-DeWitt expansion of heat kernels to an expansion of scattering phase shifts up to the first two orders.