Introduction to Quantum Mechanics · Problem 4.9

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · spherical_neumann_functions

Problem

(a) From the definition (Equation 4.46), construct

n_1(x)

and

n_2(x)

. (b) Expand the sines and cosines to obtain approximate formulas for

n_1(x)

and

n_2(x)

, valid when

x \ll 1

. Confirm that they blow up at the origin.