TY - JOUR
T1 - Quantum states of a sextic potential
T2 - Hidden symmetry and quantum monodromy
AU - Child, Mark S.
AU - Dong, Shi Hai
AU - Wang, Xiao Gang
PY - 2000/8/18
Y1 - 2000/8/18
N2 - A known terminating polynomial ansatz for a finite sub-set of states of the sextic central potential V (a, b, c; r) = ar2 + br4 + cr6, c > 0, subject to integer related parameter constraints, is confirmed to apply in two as well as three dimensions. A hidden symmetry relating the eigenstates of V (a, b, c; r) to those of V (a, -b, c; r) is used to establish the boundary between the ansatz subset and the infinite set of higher states. Connections between the radial wavefunctions Rn (a, b, c; r) and Rn′ (a, -b, c; r) also provide semiclassical insight into the origin of the parameter constraint. Finally the ansatz eigenvalue dispositions are related to the phenomenon of quantum monodromy.
AB - A known terminating polynomial ansatz for a finite sub-set of states of the sextic central potential V (a, b, c; r) = ar2 + br4 + cr6, c > 0, subject to integer related parameter constraints, is confirmed to apply in two as well as three dimensions. A hidden symmetry relating the eigenstates of V (a, b, c; r) to those of V (a, -b, c; r) is used to establish the boundary between the ansatz subset and the infinite set of higher states. Connections between the radial wavefunctions Rn (a, b, c; r) and Rn′ (a, -b, c; r) also provide semiclassical insight into the origin of the parameter constraint. Finally the ansatz eigenvalue dispositions are related to the phenomenon of quantum monodromy.
UR - http://www.scopus.com/inward/record.url?scp=0034682679&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/33/32/303
DO - 10.1088/0305-4470/33/32/303
M3 - Artículo
SN - 0305-4470
VL - 33
SP - 5653
EP - 5661
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 32
ER -