good luck

Your question is not very clearly formulated, however if you wish to know the details underlying the k.p method, the attached paper should prove helpful.

http://dx.doi.org/10.1088/0953-8984/2/49/010

If you are looking for the k·p perturbation theory it can be calculated  in degenerate case , while  for the  degenerate or nearly degenerate bands, in particular the valence bands in certain materials (such as gallium arsenide), the equations can be analyzed by the methods of degenerate perturbation theory[1,2]. Models of this type include the "Luttinger-Kohn model" (a.k.a. "Kohn-Luttinger model"),[3] and the "Kane model".[4]

As you know k·p perturbation theory is an approximation scheme for calculating the band structure  and optical properties of crystalline solids.[1,2] It is pronounced "k dot p", and is also called the "k·p method". This theory has been applied specifically in the framework of the Luttinger–Kohn model (after Joaquin Mazdak Luttinger and Walter Kohn), and of the Kane model

it can be matched with any numerical simulation  programs for any calculating

[1] P. Yu, M. Cardona (2005). Fundamentals of Semiconductors: Physics and Materials Properties (3rd ed.). Springer. Section 2.6, pp. 68 ff'. ISBN 3-540-25470-6.

[2] C. Kittel (1987). Quantum Theory of Solids (Second Revised Printing ed.). New York: Wiley. pp. 186–190. ISBN 0-471-62412-8.

[3]J. M. Luttinger, W. Kohn (1955). "Motion of Electrons and Holes in Perturbed Periodic Fields". Physical Review 97: 869. Bibcode:1955PhRv...97..869L. doi:10.1103/PhysRev.97.869.

[4]Evan O. Kane (1957). "Band Structure of Indium Antimonide". Journal of Physics and Chemistry of Solids 1: 249. Bibcode:1957JPCS....1..249K. doi:10.1016/0022-3697(57)90013-6.

Although your question a little bit is unclear, don't hesitate to contact me for any further discussion.