Use of negative complex potential as absorbing potential

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Abstract
Exact numerical calculation shows that the use of negative complex potential (NCP) significantly improves the efficiency of wavefunction absorption over that of negative imaginary potential (NIP) in scattering applications. The improvement in absorption is especially significant in the case of low energy scattering with de Broglie wavelength larger than the length of absorbing potential. The addition of a negative real potential to the pure imaginary potential speeds up the absorption of wavefunction by effectively shortening its de Broglie wavelength. Explicit TD numerical calculation for a one-dimensional model demonstrates the effectiveness of the NCP and shows that the reflection from the absorbing potential can effectively be eliminated by using optimized absorbing parameters for the energy in question. In addition, comparison of the exact numerical calculation with semiclassical WKB analysis casts a serious doubt on the quantitative value of using WKB analysis at low energies with de Broglie wavelengths much larger than the absorbing length and/or for polynomial absorbing potentials higher than linear.