Abstract
As a first application of the matrix method, the quantum mechanical behavior of the harmonic oscillator is discussed in detail.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We assume that the restoring force f is proportional to the deflection; that is, \( f = -k x\).
- 2.
Note that we get in fact
$$\varvec{AA}^\dagger - \varvec{A}^\dagger \varvec{A} = \left( \begin{array}{cccc}1&{}0&{}0&{}\cdots \\ 0&{}2&{}0&{}\cdots \\ 0&{}0&{}3&{}\cdots \\ \vdots &{}\vdots &{}\vdots &{}\ddots \end{array}\right) - \left( \begin{array}{cccc}0&{}0&{}0&{}\cdots \\ 0&{}1&{}0&{}\cdots \\ 0&{}0&{}2&{}\cdots \\ \vdots &{}\vdots &{}\vdots &{}\ddots \end{array}\right) = \left( \begin{array}{cccc}1&{}0&{}0&{}\cdots \\ 0&{}1&{}0&{}\cdots \\ 0&{}0&{}1&{}\cdots \\ \vdots &{}\vdots &{}\vdots &{}\ddots \end{array}\right) = \varvec{I}.$$
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Ludyk, G. (2018). The Harmonic Oscillator. In: Quantum Mechanics in Matrix Form. Springer, Cham. https://doi.org/10.1007/978-3-319-26366-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-26366-3_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26364-9
Online ISBN: 978-3-319-26366-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)