On the solution of the partial differential equation Πi=1N(∇2+ki2)ψ=0 Academic Article uri icon

abstract

  • It is shown that the solution of the partial differential equation Πi=1N(∇2+ki2)ψ = 0, (ki2 ≠ kj2) subject to appropriate boundary conditions may be written as ψ = Σi=1Nαiψi where the ψi's are the solutions of the Helmholtz equation (∇2 + ki2)ψi = 0 and the αi's are constants. The explicit forms of the ψi's in terms of the boundary values are also given. It is also shown that the solution of the partial differential equation (∇2 + k2)Nψ = 0 is obtained by means of a certain limiting procedure from the solution of the nondegenerate problem. Copyright © 1973 by the American Institute of Physics.

author list (cited authors)

  • Agarwal, G. S., Devaney, A. J., & Pattanayak, D. N.

citation count

  • 5

publication date

  • July 1973