Principles of Quantum Mechanics · Problem 7.5.2

The Path Integral Formulation of Quantum Theory — R. Shankar

Physics — Quantum Mechanics · hermite-polynomial-recursion

Problem

Project the relation a∣n⟩=n1/2∣n−1⟩a|n\rangle = n^{1/2}|n-1\rangle on the XX basis and derive the recursion relation Hn′(y)=2nHn−1(y)H_n'(y) = 2nH_{n-1}(y) using Eq. (7.3.22).

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