TY - JOUR

T1 - Recurrent calculations of multipole matrix elements

AU - Slavyanov, S. Yu

PY - 1999/1/1

Y1 - 1999/1/1

N2 - We propose a new method for calculating multipole matrix elements between wave eigenfunctions of the one-dimensional Schrödinger equation. The method is based on the transition to the auxiliary third- and fourth-order equations, to which an analogue of the Laplace transform is then applied. The resulting recursive procedure allows us to evaluate matrix elements starting with a number of eigenvalues that are assumed to be known and several basis matrix elements. As an example, we consider the multipole matrix elements between the wave functions of the harmonic and nonharmonic oscillators.

AB - We propose a new method for calculating multipole matrix elements between wave eigenfunctions of the one-dimensional Schrödinger equation. The method is based on the transition to the auxiliary third- and fourth-order equations, to which an analogue of the Laplace transform is then applied. The resulting recursive procedure allows us to evaluate matrix elements starting with a number of eigenvalues that are assumed to be known and several basis matrix elements. As an example, we consider the multipole matrix elements between the wave functions of the harmonic and nonharmonic oscillators.

UR - http://www.scopus.com/inward/record.url?scp=0033234810&partnerID=8YFLogxK

U2 - 10.1007/BF02557244

DO - 10.1007/BF02557244

M3 - Article

AN - SCOPUS:0033234810

VL - 120

SP - 1213

EP - 1219

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 3

ER -