The Li ion (a single electron, ) is hydrogen-like

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · Central potentials and canonical three-dimensional systems

The Structure of Quantum Mechanics, Ch Hydrogen, and the symmetry that explains it

Problem

The Li

^{2+}

ion (a single electron,

Z=3

) is hydrogen-like. The Casimir relation derived from the

SO(4)

algebra,

\hat K^2+\hat L^2=(n^2-1)\hbar^2,

holds for any hydrogen-like ion, since it follows from the representation theory of the algebra and not from the value of

Z

. Consider the

4f

state of Li

^{2+}

(

n=4

l=3

). Find

\langle \hat K^2\rangle

for this state, in units of

\hbar^2

Related theory

Quantum Mechanics

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