Abstract
In this chapter we shall review the spectral properties of the harmonic oscillator, i.e. 3 of the operator given by the Weyl-quantization of the Hamiltonian (|ξ|2, + |x|2)/2
Keywords
- Harmonic Oscillator
- Orthonormal Basis
- Poisson Bracket
- Symplectic Form
- Closed Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Berlin Heidelberg
About this chapter
Cite this chapter
Parmeggiani, A. (2010). The Harmonic Oscillator. In: Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction. Lecture Notes in Mathematics(), vol 1992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11922-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-11922-4_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11921-7
Online ISBN: 978-3-642-11922-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
