An electron is in an orbital state with

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

l = 4

. Recalling Bohr's rule

L = n\hbar

, a student writes down the length of the orbital angular momentum as

4\hbar

. ((a)) Using the eigenvalue of

\hat L^2

, give the true length

|\mathbf L|

as a multiple of

\hbar

to three significant figures. ((b)) By what percentage of the true length does this

4\hbar

fall short? Give the answer to three significant figures. ((c)) What is the largest value a measurement of

L_z

can give in this state, as a multiple of

\hbar

? ((d)) What is the smallest angle between

\mathbf L

and the

z

axis, in degrees to three significant figures?