Principles of Quantum Mechanics

Chapter 4

Operators, Eigenstates, Eigenvalues and Schrodinger Equation

If Quantum Mechanics has not profoundly shocked you, you have not understood it yet.

—Niels Bohr

4.1  INTRODUCTION

We have learnt in the previous Chapter that it is consistent to visualize a microscopic particle (under all circumstances) as some form of (matter) wave. We shall represent these matter waves by the space- and time-dependent wave function ψ(r, t). In the previous chapter, we had represented the classical waves and wave packets by wave displacements y(r, t). In this chapter, we shall develop the concept of operators, operating on the wave function (or eigenstate) ψ(r, t) and providing information about their eigenvalues. We shall study how to write down the equation ...