ABSTRACT
Exact solution of Schrödinger equation can be obtained for a simple system like hydrogen atom (one electron system), but for atoms having more than one electron, difficulties arise in solving the Schrödinger equation. Under the circumstances, this chapter describes a systematic general approach for obtaining approximate solutions to the Schrödinger equation. The approximate methods discussed here are the perturbation method and variation method. This chapter first deals with the perturbation method/theory for nondegenerate states. According to this method, a chemical system is subjected to an electric or a magnetic field so that it becomes perturbed. This chapter begins with first-order perturbation for correction to energy and wave function. After this, it deals with the second-order perturbation for correction to energy and wave function, and it also gives knowledge of bra–ket notation for simplicity sake in place of integration and this notation has been employed in obtaining the first- and second-order corrections to energy and wave function of a system. It also describes the perturbation theory for a degenerate case for getting both first- and second-order energy corrections and wave functions. This chapter also deals with application of perturbation theory to anharmonic oscillator and electronic polarisibility of hydrogen atom. This chapter also describes the application of perturbation theory to He atom for obtaining the first- and second-order corrections to energy. This chapter also provides the proof of variation theorem, computation of energy Eigen value and wave function by variation method. The variation method has been lucidly applied in the estimation of energy of the ground state of simple harmonic oscillator. It also discusses the ground state of He atom and ground state of H atom for which a trial function is used. Like other chapters, it also provide references, a number of solved problems on both approximate methods. A large number of questions on concepts have been given for exercise to readers so that they become expertise in computational problems.
