THE SCHRÖDINGER EQUATION

Abstract

Publisher Summary This chapter discusses the Schrödinger equation. The postulates of the quantum theory constitute the foundation of quantum mechanics. One of their consequences is the Schrodinger equation for stationary states of the molecule. In the time-independent Schrödinger equation stationary states can be produced as solutions of the equation. The time-dependent Schrödinger equation plays a pivotal role as the equation of motion. The Schrödinger equation also describes the evolution of a given wave function. Both the stationary states and the evolution of the non-stationary states depend on the energy operator (Hamiltonian). Wave function is a central notion in quantum mechanics. The chapter reviews the symmetry of the Hamiltonian and its consequences. The Schrödinger equation is a differential equation. In order to obtain a special solution to such equations, one has to insert particular boundary conditions to be fulfilled. The Schrödinger equation for stationary states and the time-dependent Schrödinger equation are also discussed.