A particle in orbital motion is in a state for which a measurement of (the squared…
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Orbital angular momentum, the spherical harmonics and rotations
Problem
A particle in orbital motion is in a state for which a measurement of L2 (the squared length of the orbital angular momentum) is certain to give 30ℏ2, where ℏ is the reduced Planck constant. Translate this statement into the labels and numbers of the ladder scheme.
((a)) What is the quantum number l?
((b)) How many different values may a measurement of Lz give in this state?
((c)) What is the largest of those values, as a multiple of ℏ?
((d)) What is the smallest possible angle between the angular momentum vector and the z axis, in degrees to three significant figures?