abstract

• The Schrödinger equation with the trigonometric Rosen-Morse potential in a flat three-dimensional Euclidean space, E3, and its exact solutions are shown to be exactly Fourier transformable to momentum space, though the resulting equation is purely algebraic and cannot be cast into the canonical form of an integral Lippmann-Schwinger equation. This is because the cotangent function does not allow for an exact Fourier transform in E 3. In addition, we recall that the above potential can also be viewed as an angular function of the second polar angle parametrizing the three-dimensional spherical surface, S3, of a constant radius, in which case the cotangent function would allow for an exact integral transform to momentum space. On that basis, we obtain a momentum space Lippmann-Schwinger- type equation, though the corresponding wavefunctions have to be obtained numerically. © 2011 IOP Publishing Ltd.

authors

• Arenhovel Kirchbach Mariana Nikolova
• Compean C.B.

publication date

• 2011-01-01

published in

• Journal of Physics A: Mathematical and Theoretical  Journal

Digital Object Identifier (DOI)

• 10.1088/1751-8113/44/1/015304

start page

end page

volume

• 44

issue

• 1