A Method to Calculate a Delta Function of the

We propose a new method to calculate expectation values of a delta function of the Hamiltonian, Ψ | δ(ˆ H − E) | Ψ. Since the delta function can be replaced with a Gaussian function, we evaluate Ψ | β π e −β(ˆ H−E) 2 | Ψ with large β adopting the Suzuki-Trotter decomposition. Errors of the approximate calculations with the finite Trotter number N t are estimated to be O(1/N K t) for the Kth-order decomposition. The distinct advantage of this method is that the convergence is guaranteed even when the state | Ψ contains the eigenstates whose energies spread over the wide range. In this paper we give a full description of our method within the quantum mechanical physics and present the numerical results for the harmonic oscillator problems in one-and three-dimensional space.