A remark to quasilinearization

Quasilinearization approach to quantum mechanics

The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schrödinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was discussed recently by one of the present authors (VBM), approaches the solution of a nonlinear differential equation by approximating the nonlinear terms by a seq...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Quasilinearization Approach to Nonlinear Problems in Physics

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method could be proved are formulated and elaborated. The method, whose mathematical basis in physics was discussed recently by one of the present authors (VBM), approximates the solution of a nonlinear differential equation by treating the nonlinear terms as a perturbation about the li...

Quasilinearization method and WKB

Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. While the WKB method generates an expansion in powers of h̄, the quasilinearization method (QLM) approaches the solution of the nonlinear equation obtained by casting the Schrödinger equation into the Riccati form by approximating nonlinear terms by a sequence of linear ones. It does not rely on the ex...

Answer to Prof. Störmer's Remark.

1 For references to the work of Friedman, LeMaitre, Robertson, Tolman, Eddington and de Sitter in this field, see Tolman, Proc. Nat. Acad. Sci., 16, 582 (1930). 2 Stern, Zeits. Electrochem., 31, 448 (1925); Trans. Faraday Soc., 21, 477 (1925-26). 8 Tolman, Proc. Nat. Acad. Sci., 12, 670 (1926). 4Tolman, Phys. Rev., 35, 904 (1930). Tolman, Proc. Nat. Acad. Sci., 14, 353 (1928). 6 Tolman, Ibid., ...