For scalar, electromagnetic, or gravitational wave propagation on a background Schwarzschild blackhole, we describe the exact nonlocal radiation outer boundary conditions (robc) appropriate for a spherical outer boundary of finite radius enclosing the blackhole. Derivation of the robc is based on Laplace and spherical– harmonic transformation of the Regge–Wheeler equation, the pde governing the...

The well-known Heun equation has the form { Q(z) d2 dz2 + P (z) d dz + V (z) } S(z) = 0, where Q(z) is a cubic complex polynomial, P (z) and V (z) are polynomials of degree at most 2 and 1 respectively. One of the classical problems about the Heun equation suggested by E. Heine and T. Stieltjes in the late 19-th century is for a given positive integer n to find all possible polynomials V (z) su...

The harmonic Lagrange top is the plus a quadratic (harmonic) potential term. We describe in space fixed frame using global description with Poisson structure on \(T^{*}S^{3}\). This naturally leads to rational parametrisation of set critical values energy-momentum map. show that there are 4 different topological types for generic parameter values. quantum mechanics described by most general con...