# Harmonic Oscillator Basis States

Keywords: Quantum Mechanics, Harmonic Oscillator, Basis States, Dirac Notation, Eigenvectors

### Highlights of the activity

1. Students express the normalization condition for harmonic oscillator states in Dirac notation and in wave function notation
2. Students express the orthogonality condition for harmonic oscillator states in Dirac notation and in wave function notation
3. Students express the completeness condition for harmonic oscillator states in Dirac notation and in wave function notation

### Reasons to spend class time on the activity

This small whiteboard activity reviews the properties of normalization, orthogonality, and completeness that all basis states possess. Students write down each of the three properties for the energy eigenstates of the harmonic oscillator, both in Dirac notation and in wave function notation. This activity prepares students for calculations in the harmonic oscillator system.

### Instructor's Guide

Authors: David H. McIntyre
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