TY - JOUR
T1 - Explicit Relations of Physical Potentials Through Generalized Hypervirial and Kramers' Recurrence Relations
AU - Sun, Guo Hua
AU - Dong, Shi Hai
N1 - Publisher Copyright:
© 2015 Chinese Physical Society and IOP Publishing Ltd.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - Based on a Hamiltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchard-like (non-diagonal case) and Kramers' (diagonal case) recurrence relations for arbitrary xκ which is independent of the central potential V(x). Some significant results in diagonal case are obtained for special κ in xκ (κ ≥ 2). In particular, we find the orthogonal relation 〈n1|n2〉 = δn1n2 (κ = 0), 〈n1|V′(x)|n2〉 = (En1 - En2)2〈n1|x| n2〉 (κ = 1), En = 〈n|V′ (x)x/2|n〉 + 〈n|V(x)|n〉 (κ = 2) and -4En〈n|x|n〉 + 〈n|V′(x)x2|n〉 + 4〈n|V(x)x|n〉 = 0 (κ = 3). The latter two formulas can be used directly to calculate the energy levels. We present useful explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.
AB - Based on a Hamiltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchard-like (non-diagonal case) and Kramers' (diagonal case) recurrence relations for arbitrary xκ which is independent of the central potential V(x). Some significant results in diagonal case are obtained for special κ in xκ (κ ≥ 2). In particular, we find the orthogonal relation 〈n1|n2〉 = δn1n2 (κ = 0), 〈n1|V′(x)|n2〉 = (En1 - En2)2〈n1|x| n2〉 (κ = 1), En = 〈n|V′ (x)x/2|n〉 + 〈n|V(x)|n〉 (κ = 2) and -4En〈n|x|n〉 + 〈n|V′(x)x2|n〉 + 4〈n|V(x)x|n〉 = 0 (κ = 3). The latter two formulas can be used directly to calculate the energy levels. We present useful explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.
KW - Hamiltonian identity
KW - Kramers' recurrence relation
KW - hypervirial relations
KW - physical potentials
UR - http://www.scopus.com/inward/record.url?scp=84935924343&partnerID=8YFLogxK
U2 - 10.1088/0253-6102/63/6/682
DO - 10.1088/0253-6102/63/6/682
M3 - Artículo
SN - 0253-6102
VL - 63
SP - 682
EP - 686
JO - Communications in Theoretical Physics
JF - Communications in Theoretical Physics
IS - 6
M1 - 682
ER -