Magnetic WKB Constructions

Accuracy of the WKB

Microlocal WKB expansions

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...

Multicomponent WKB and Quantization

Hamiltonians whose symbols are not simply real valued, but matrix or, more generally, endomorphism valued functions appear in many places in physics, examples being the Dirac equation, multicomponent wave equations like electrodynamics in media, and Yang-Mills theories, and the Born-Oppenheimer approximation in molecular physics. Whereas the semiclassical and WKB approximation of scalar systems...

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...