TY - JOUR
T1 - Generalized hypervirial and Blanchard's recurrence relations for radial matrix elements
AU - Dong, Shi Hai
AU - Chen, Chang Yuan
AU - Lozada-Cassou, M.
PY - 2005/7/14
Y1 - 2005/7/14
N2 - Based on the Hamiltonian identity, we propose a generalized expression of the second hypervirial for an arbitrary central potential wavefunction in arbitrary dimensions D. We demonstrate that the new proposed second hypervirial formula is very powerful in deriving the general Blanchard's and Kramers' recurrence relations among the radial matrix elements. As their useful and important applications, we derive all general Blanchard's and Kramers' recurrence relations and some identities for the Coulomb-like potential, harmonic oscillator and Kratzer oscillator. The recurrence relation and identity between the exponential functions and the powers of the radial function are established for the Morse potential. The corresponding general Blanchard's and Kramers' recurrence relations in 2D are also briefly studied.
AB - Based on the Hamiltonian identity, we propose a generalized expression of the second hypervirial for an arbitrary central potential wavefunction in arbitrary dimensions D. We demonstrate that the new proposed second hypervirial formula is very powerful in deriving the general Blanchard's and Kramers' recurrence relations among the radial matrix elements. As their useful and important applications, we derive all general Blanchard's and Kramers' recurrence relations and some identities for the Coulomb-like potential, harmonic oscillator and Kratzer oscillator. The recurrence relation and identity between the exponential functions and the powers of the radial function are established for the Morse potential. The corresponding general Blanchard's and Kramers' recurrence relations in 2D are also briefly studied.
UR - http://www.scopus.com/inward/record.url?scp=21044432512&partnerID=8YFLogxK
U2 - 10.1088/0953-4075/38/13/013
DO - 10.1088/0953-4075/38/13/013
M3 - Artículo
SN - 0953-4075
VL - 38
SP - 2211
EP - 2220
JO - Journal of Physics B: Atomic, Molecular and Optical Physics
JF - Journal of Physics B: Atomic, Molecular and Optical Physics
IS - 13
ER -