Browsing by Author "Karwowski, Jacek"

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Analytical Solutions of the Schrodinger Equation with Power Potentials
(2016-01-01)
Karwowski, Jacek
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
Conditions for the existence of polynomial solutions of the Schrodinger equation with potentials which are linear combinations of powers of r ranging from -2 to 2m, where m is a non-negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.
Analytical Solutions of the Schrodinger Equation with Power Potentials
(2016-01)
Karwowski, Jacek
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
Conditions for the existence of polynomial solutions of the Schrodinger equation with potentials which are linear combinations of powers of r ranging from -2 to 2m, where m is a non-negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.
Biconfluent Heun equation in quantum chemistry: Harmonium and related systems
(2014-05-11)
Karwowski, Jacek
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
Schrodinger equation for harmonium and related models may be transformed to the biconfluent Heun equation. The solubility of this equation and its applications in quantum chemistry are briefly discussed.
Schrodinger equations with power potentials
(2016-04-17)
Karwowski, Jacek
;
Witek, Henryk A.
;
應用化學系
;
應用化學系分子科學碩博班
;
Department of Applied Chemistry
General formulae for solutions of the Schrodinger equation with power potentials are derived. The wavefunctions are expressed as products of the asymptotic factors and special forms of the Hessenberg determinants, in general, of infinite order. Conditions under which the order of the determinants becomes finite are determined. It is shown that solutions represented by the finite-order determinants may exist only if the highest power of the radial variable in the potential function is even. [GRAPHICS] .