|
|
|
|
|
|
 |
 |
|
Spectral Zeta Functions
|
|
|
|
|
|
| Organization: | University of Western Australia |
|
|
|
|
|
|
Wolfram Technology Conference 2014
|
|
|
|
|
|
Champaign, Illinois, USA
|
|
|
|
|
|
When the eigenvalues of an operator A can be computed and form a discrete set the spectral zeta function of A reduces to a sum over eigenvalues, when the sum exists (see Berry [1], Elizalde [2], and Crandall [3]). Belloni and Robinett [4] used the “quantum bouncer” to compute quantum sum rules (see Vallée and Soares [5]). Here we use Mathematica to compute the spectral zeta function for various special functions via the Weierstrass product theorem.
References
[1] Berry M V 1986 “Spectral zeta functions for Aharonov-Bohm quantum billiards” J. Phys. A: Math. Gen. 19 2281-96 [2] Elizalde E 1995 Ten physical applications of spectral zeta functions (Berlin: Springer) [3] Crandall R E 1996 “On the quantum zeta function” J. Phys. A: Math. Gen. 29 6795-6816 [4] Belloni M and Robinett R W 2009 “Constraints on Airy function zeros from quantum-mechanical sum rules” J. Phys. A 42 075203 [5] Vallée O and Soares M 2004 Airy functions and applications to physics (London: Imperial College Press)
|
|
|
|
|
|
|
|
|
|
|
|
http://www.wolfram.com/events/technology-conference/2014
|
|
|
|
|
|
| WTC14SpectralZeta_PaulAbbot.cdf (2.6 MB) - CDF Document |
|
|
|
|
|
|
|
| | | | | |
|
For the newest resources, visit Wolfram Repositories and Archives »
