Chapter 4
Back and Forth with Harmonic Oscillators
In This Chapter
Hamiltonians: Looking at total energy
Solving for energy states with creation and annihilation operators
Understanding the matrix version of harmonic oscillator operators
Writing computer code to solve the Schrödinger equation
Harmonic oscillators are physics setups with periodic motion, such as things bouncing on springs or tick-tocking on pendulums. You’re probably already familiar with harmonic oscillator problems in the macroscopic arena, but now you’re going microscopic. There are many, many physical cases that can be approximated by harmonic oscillators, such as atoms in a crystal structure.
In this chapter, you see both exact solutions to harmonic oscillator problems as well as computational methods for solving them. Knowing how to solve the Schrödinger equation using computers is a useful skill for any quantum physics expert.
Grappling with the Harmonic Oscillator Hamiltonians
Okay, time to start talking Hamiltonians (and I’m not referring to fans of the U.S. Founding Father Alexander Hamilton). The Hamiltonian ...
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