I was reading through my Principles of Quantum Mechanics textbook and arrived at the section that discusses the quantum harmonic oscillator. In this discussion the equation ψ"-(y^2)ψ=0 presents itself and a solution is given as ψ=(y^m)*e^((-y^2)/2), similar to a gaussian function i assume. My book has given no derivation that yielded this answer it only supplied it, so my question is if an answer of this sort can be algebraically solved for, or what kind of logic would lead to such an answer. Thank you in advance for any responses.(adsbygoogle = window.adsbygoogle || []).push({});

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# Quantum Harmonic Oscillator necessary DE

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