Excited States of Quantum Harmonic Oscillator using Raising Operator

Calculating Excited States of Quantum Harmonic Oscillator using Raising Operator.

The ground state of a simple quantum harmonic oscillator is a Gaussian function. Raising operator is formed using a finite difference operator, and when acted on ground state wave function, produces excited states. At the end, three excited levels are plotted along with the ground state. All the constants like m, omega or h bar are omitted for simplicity. All equations relevant to this program have been referred from Chapter 2 of Griffiths book.