Slater sum for the one-dimensional <tex>$sech^{2}$</tex> potential in relation to the kinetic energy density
Slater sum for the one-dimensional <tex>$sech^{2}$</tex> potential in relation to the kinetic energy density
Faculty of Sciences. Physics

article

2004
New York, N.Y.
, 2004

Physics

Journal of mathematical physics. - New York, N.Y.

45(2004)
:6
, p. 2411-2419

0022-2488

000221658500022

E

English (eng)

University of Antwerp

In earlier work on the one-dimensional sech(2) potential energy [I. A. Howard and N.H. March, Int. J. Quantum Chem. 91, 119 (2003)] it has been shown that both electron density rho(x) and kinetic energy t(x) are low-order polynomials in the potential V(x), for a small number of bound states. Here all attention is focused on the continuum states for the sech(2) potential with a single bound state. The tool employed is the Slater sum, which satisfies a partial differential equation. This is first solved explicitly for the bound state, and then the solution is generalized to apply to the continuum. Again, considerable simplification is exhibited for this specific choice of potential. A brief discussion is included of a central sech(2)(r) potential. (C) 2004 American Institute of Physics.

https://repository.uantwerpen.be/docman/iruaauth/d55261/7794180.pdf

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