Abstract
Surfaces, interfaces, thin films, and quantum wires provide abundant examples of quasi two-dimensional or one-dimensional systems in science and technology. Quantum mechanics in low dimensions has become an important tool for modeling properties of these systems. Here we wish to go beyond the simple low-dimensional potential models of Chapter 3 and discuss in particular implications of the dependence of energy-dependent Green’s functions on the number d of spatial dimensions.
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.
These concepts are further discussed in Appendix I. However, it is not necessary to read Appendix I before reading this section.
- 2.
For spin or helicity, there is actually a transition from a tensor product to a trace operation in making the connection between (20.15) and (20.16): \(1 ={ \sum \nolimits }_{s}\vert s\rangle \langle s\vert \rightarrow {\sum \nolimits }_{s}\langle s\vert s\rangle = g\). Otherwise equation (20.16) would yield the density of states per spin state.
- 3.
R. Dick, Physica E 40, 2973 (2008); Nanoscale Res. Lett. 5, 1546 (2010).
- 4.
R. Dick, Int. J. Theor. Phys. 42, 569 (2003). See also the previous references.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Dick, R. (2012). Dimensional Effects in Low-dimensional Systems. In: Advanced Quantum Mechanics. Graduate Texts in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8077-9_20
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8077-9_20
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-8076-2
Online ISBN: 978-1-4419-8077-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)