Word Count : 209

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To solve for \(\psi_3(x)\) using the recursive equation: \[ \psi_{n+1}(x) = \sqrt{\frac{2}{n+1}} x \psi_n(x) - \sqrt{\frac{n}{n+1}} \frac{d}{dx} \psi_n(x), \] we need the value of \(\psi_2(x)\) and its derivative \(\frac{d}{dx} \psi_2(x)\). ### Step-by-step Solution: 1. Start with \(\psi_0(x)\) and \(\psi_1(x)\): Usually, \(\psi_0(x)\) ___ ____ ________ __________ _________ ____ _____ ________ ___ _________ ___ ____.
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