Quantum Mechanical Treatment of the Simple Harmonic Oscillator

The chapter discusses the quantum mechanical treatment of a simple harmonic oscillator by using the Dirac method of raising and lowering operators. Successive applications of these operators respectively raise and lower the eigen-values of the energy. Further application of the lowering operator is not possible, and it is this clue that allows to calculate the solutions of the wave function. This gives the ground-state energy of a simple harmonic oscillator. Returning to the operation of the lowering operator on the ground-state wave function allows solution of the wave function. The chapter also discusses a selection rule of optical transitions between the states of the simple harmonic oscillator.