Principles of Quantum Mechanics

Chapter 8

Linear Harmonic Oscillator—Revisited

8.1  INTRODUCTION

One-dimensional harmonic oscillator problem was studied in Chapter 6, where Schrodinger equation was solved using the power series method. This method is a bit lengthy but it has the virtue that same strategy may be applicable to other potentials, for example, Coulomb potential (which we shall discuss in Chapter 10, in the context of Hydrogen atom). The second method of solving Schrodinger equation for harmonic oscillator is the algebraic technique using the so-called annihilation and creation operators or lowering and raising operators or ladder operators. This method is really quicker and simpler too (in comparison to the power series method). This technique shall also be used ...