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Spectral approximation by the polar transformation


Spectral approximation by the polar transformation

Zhou, Wei Hua (1997) Spectral approximation by the polar transformation. Masters thesis, Concordia University.



Central potentials V(r) are considered which admit the polar representation $V(r)=g(h(r)),$ where $h(r)={\rm sgn}(q)r\sp{q},$ q is fixed, and g is the polar transformation function. This representation allows the Schrodinger eigenvalues generated by V to be approximated in terms of those generated by the polar potential h(r). In many cases the optimal values $\{q\sb1,q\sb2\}$ of the power q can be chosen so that the corresponding polar functions $\{g\sb1,g\sb2\}$ have definite and opposite convexity. For such cases the spectral approximations provide both upper and lower bounds for the entire discrete spectrum. The example of the central potential $V(r)=ar\sp2+br\sp2/(1+cr\sp2)$ in $R\sp3$ is studied in detail: optimal bounds are determined for a wide range of the potential parameters. The method is applicable, essentially unchanged, for problems in any number of spatial dimensions.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Zhou, Wei Hua
Pagination:vi, 56 leaves ; 29 cm.
Institution:Concordia University
Degree Name:Theses (M.Sc.)
Program:Dept. of Mathematics and Statistics
Thesis Supervisor(s):Hall, Richard L.
ID Code:263
Deposited By: Concordia University Libraries
Deposited On:27 Aug 2009 17:10
Last Modified:08 Dec 2010 15:13
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