Using the recursion

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · Wave mechanics in one dimension

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The harmonic oscillator

Problem

Using the recursion bj+2=2j+1−ε(j+1)(j+2)bjb_{j+2} = \dfrac{2j+1-\varepsilon}{(j+1)(j+2)}b_j, show that ε=9\varepsilon = 9 stops the even series (b0≠0b_0\ne0) after b4b_4, find the polynomial gg this gives, identify nn, and give the energy EE in units of ℏω\hbar\omega.

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