A particle of mass is bound in an attractive central potential that supports several…
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Central potentials and canonical three-dimensional systems · Central potentials and canonical three-dimensional systems
The Structure of Quantum Mechanics, Ch Central potentials as a rotation problem
Problem
A particle of mass m is bound in an attractive central potential V(r) that supports several s-wave (l=0) bound states. Three of the normalised reduced radial functions u(r) are found, numerically, to have 2, 0 and 1 nodes respectively for r>0; call these uX, uY and uZ.
((a)) State the node theorem for l=0 bound states of an attractive potential.
((b)) Order the energies EX, EY, EZ from lowest to highest.