
SIGMA 3 (2007), 057, 6 pages arXiv:0704.2679
http://dx.doi.org/10.3842/SIGMA.2007.057
Contribution to the Vadim Kuznetsov Memorial Issue
On the Applications of a New Technique to Solve Linear Differential Equations, with and without Source
N. Gurappa ^{a}, Pankaj K. Jha ^{b} and Prasanta K. Panigrahi ^{c}
^{a)} Saha Institute of Nuclear Physics, Bidhannagar, Kolkata 700 064, India
^{b)} Department of Physics, Texas A M University, TX 77843, USA
^{c)} Physical Research Laboratory, Navrangpura, Ahmedabad 380 009, India
Received November 01, 2006, in final form March
29, 2007; Published online April 20, 2007
Abstract
A general method for solving linear differential equations of
arbitrary order, is used to arrive at new representations for the
solutions of the known differential equations, both without and with a
source term. A new quasisolvable potential has also been constructed
taking recourse to the above method.
Key words:
Euler operator; monomials; quasiexactly solvable models.
pdf (176 kb)
ps (144 kb)
tex (9 kb)
References
 Adomian G., Solving Frontier Problems of physics: the
decomposition method, Kluwer, Dordrecht, 1994.
 Atre R., Mohapatra C.S., Panigrahi P.K., Finding exact and approximate wave functions
of Hooke's atom, their information entropy and correlation, Phys. Lett. A
361 (2007), 3338.
 Christ N.H., Lee T.D., Quantum expansion of soliton solutions, Phys. Rev. D
12 (1975), 16061627.
 Gradshteyn I.S., Ryzhik I.M., Tables of
integrals, series and products, Academic Press Inc., 1965.
 Gurappa N., Khare A., Panigrahi P.K., Connection between CalogeroMarchioroWolfes
type fewbody models and free oscillators, Phys. Lett. A 244 (1998),
467472, condmat/9804207.
 Gurappa N., Panigrahi P.K., Free harmonic oscillators, Jack polynomials, and
CalogeroSutherland systems, Phys. Rev. B 62 (2000), 19431949,
hepth/9910123.
 Gurappa N., Panigrahi P.K, On polynomial solutions of the Heun
equation, J. Phys. A: Math. Gen. 37 (2004), L605L608,
mathph/0410015.
 Gurappa N., Panigrahi P.K., Shreecharan T., A new perspective on single and
multivariate differential equations, J. Comput. Appl. Math. 160 (2003), 103112.
 Jatkar D.P., Kumar C.N., Khare A., A quasiexactly solvable problem
without SL(2) symmetry, Phys. Lett. A 142 (1989), 200202.

