An extended class of L2-series solutions of the wave equation

Details An extended class of L2-series solutions of the wave equation An extended class of L2-series solutions of the wave equation

2004-08-31

arxiv.org/abs/quant-ph/0409002v1

Ann. Phys. 317.1 (2005) 152-174

Physics

Quantum Physics

18 pages, 1 figure

Scientific paper

10.1016/j.aop.2004.11.014

We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such includes the discrete (for bound states) as well as the continuous (for scattering states) spectrum of the Hamiltonian. The problem translates into finding solutions of the resulting three-term recursion relation for the expansion coefficients of the wavefunction. These are written in terms of orthogonal polynomials, some of which are modified versions of known polynomials. The examples given, which are not exhaustive, include problems in one and three dimensions.

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