Time-to-energy transform of wavepackets using absorbing potentials. Time-independent wavepacket-Schrödinger and wavepacket-Lippmann—Schwinger equations

✍ Scribed by Donald J. Kouri; Mark Arnold; David K. Hoffman

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 762 KB
• Volume: 203
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(93)85382-x

✦ Synopsis

It is shown that one may use an Lz basis, matrix representation of the Hamiltonian, including a negative imaginary absorbing potential, to carry out arbitrarily long-time evolution of wavepackets. The time-t&energy Fourier transform of the wavepacket is carried out analytically, yielding a new type of time-independent scattering equation in which the "source" of scattered waves is the initial (t=O) L1 wavepacket used in the time-dependent propagation. Alternatively, one obtains the analogous time-independent, inhomogeneous wavepacket-Schtiinger equation. A banded representation of the Hamiltonian is achieved by the use of distributed approximating function theory to evaluate the kinetic energy. The resulting new time-independent wavepacket equations are solved both by matrix diagonalization of the Hamiltonian, and as inhomogeneous linear algebraic equations. The ap proach is illustrated by application to electron scattering (in one dimension) by a double barrier potential.