Calculation of the Approximate Energy of Ground and Excited Stationary States in Quantum Mechanics Using Delta Method

Abstract

In this paper, pursuing a new advised method called Delta method which is basically similar to variational method, we find the ground and excited states, according to a typical quantum Hamiltonian. Moreover, applying this method, the upper bound values for the eigenenergies of the socalled ground and excited states are estimated. We will show that this new method, is as beneficial as the traditional variational method which is common in deriving eigenenergies of some of the quantum Hamiltonians. This method helps physics students to broaden their knowledge about the possible mathematical ways; they can use to obtain eigenenergies of some quantum Hamiltonians. The advantage of Delta method to variational method is in its simplicity and reduction of the calculation procedures.

Development and refinement of the Variational Method based on Polynomial Solutions of Schrödinger Equation

“…Payandeh and Mohammadpour used the Delta method to evaluate the energy of ground and excited stationary states in quantum mechanics. The advantage of the Delta method compared to the variational method is its simplicity and reduction of the calculation procedures [18]. P. M. Gaiki and P. M. Gade [19] demonstrated how a freeware, SAGE, can be employed for the variational solution of simple and complex Hamiltonians in one dimension to estimate the ground state energy.…”