A particle of mass m moves in a parabolic potential, Ask an Expert

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A particle of mass m moves in a parabolic potential (energy): \(V(x) = \frac{1}{2} m\omega_{0}^{2}x^{2}\)

(a)(Griffiths Intro to QM, 2nd ed) finds the first excited state \(\psi_{1}(x)\)

Use the ladder operator a+ to find the second excited state wave function \(\psi_{2}(x)\)

(b) Demonstrate the orthogonality of the states \(\psi_{0}(x), \psi_{1}(x),and\psi_{2}(x)\) by direct integration.

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