(For ? = 1 / 2 the last terms in these formulas drop out completely; see the spherical Bessel functions above . ) Even though these equations are true, better approximations may be available for complex " z ".
12.
In the standard scattering problem, the incoming beam is assumed to take the form of a plane wave of wave number, which can be decomposed into partial waves using the plane wave expansion in terms of spherical Bessel functions and Legendre polynomials:
13.
In case where the potential well is infinitely deep, so that we can take V _ 0 = 0 inside the sphere and \ infty outside, the problem becomes that of matching the wavefunction inside the sphere ( the spherical Bessel functions ) with identically zero wavefunction outside the sphere.
