Quasilinearization method and WKB

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...

Divergence-free WKB method.

A new semiclassical approach to the linear and nonlinear one-dimensional Schrödinger equation is presented. For both equations our zeroth-order solutions include nonperturbative quantum corrections to the WKB solution and the Thomas-Fermi solution, thereby allowing us to make uniformly converging perturbative expansions of the wave functions. Our method leads to a new quantization condition tha...

Unruh Radiation via WKB Method

Abstract Generalized Quasilinearization Method for Coincidences

Generalized Quasilinearization Method for Coincidences Adriana Buică and Radu Precup Faculty of Mathematics and Computer Science Babeş-Bolyai University 3400 Cluj, Romania [email protected], [email protected] Abstract An abstract unified theory of both monotone iterative and generalized quasilinearization methods is presented for operator equations of coincidence type in ordered Ban...

Development of the Method of Generalized Quasilinearization

The method of Quasilinearization which was developed by Bellman and Kalaba covers the situation when the forcing function is either convex or concave. Here, we describe the process of the Quasilinearization method being extended, refined and generalized so as to include forcing functions which are the sum of a convex and concave function. This includes many special cases which are extensions of...