In finding eigenvalues by solving differential equations, quantization occurs only when we apply the condition that the

Question:

In finding eigenvalues by solving differential equations, quantization occurs only when we apply the condition that the eigenfunctions be well behaved. Ladder operators were used in Section 5.4 to find the eigenvalues of and and in Prob. 5.36 to find the harmonic-oscillator energy eigenvalues. Where was the condition that the eigenfunctions be wellbehaved used in the derivations in Section 5.4 and Prob. 5.36? See Prob. 7.11.