The semiclassical method of torus quantization is just the first term of a certain h̄-expansion, usually called the WKB expansion. The method goes back to the early days of quantum mechanics and was developed by Bohr and Sommerfeld for onefreedom systems and separable systems, it was then generalized for integrable (but not necessarily separable) systems by Einstein [1], which is called EBK or t...

WKB p-forms are constructed as approximate solutions to boundary value problems associated with semi-classical Witten Laplacians. Naturally distorted Neumann or Dirichlet boundary conditions are considered. MSC 2000: 58J37 (58J10 58J32 81Q20)

The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.

We provide a semiclassical theory of tunneling decay in a magnetic field and a three-dimensional potential of a general form. Because of broken time-reversal symmetry, the standard WKB technique has to be modified. The decay rate is found from the analysis of the Hamilton trajectories of the particle in complex phase space and time. In a magnetic field, the tunneling particle comes from beneath...

We investigate the system of a particle moving on a half line x ≥ 0 under the general walls at x = 0 that are permitted quantum mechanically. These quantum walls, characterized by a parameter L, are shown to be realized as a limit of regularized potentials. We then study the classical aspects of the quantum walls, by seeking a classical counterpart which admits the same time delay in scattering...