January 2013
Beginner to intermediate
336 pages
6h 6m
English
Content preview from Quantum Physics For Dummies, Revised Edition
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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 will let you find the energy levels of a system.
Going classical with harmonic oscillation
In classical terms, the force on an object in harmonic oscillation is the following (this is Hooke's law):
F = −kx
In this equation, k is the spring constant, measured in Newtons/meter, and x is displacement. The key point here is that the restoring force on whatever is in harmonic motion is proportional ...
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O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.