Journal
ANNALS OF PHYSICS
Volume 409, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2019.167930
Keywords
Potential energy matrix; Oscillator basis; Eigenvalue; Eigenfunction; Separable representation
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Funding
- Program of Fundamental Research of the Physics and Astronomy Department of the National Academy of Sciences of Ukraine [0117U000239]
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Matrix elements of potential energy are examined in detail. We consider a model problem - a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and L-2 basis (J-matrix) method for the quantum theory of scattering. (C) 2019 Elsevier Inc. All rights reserved.
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