I'm reading Griffiths', and I had a question about the harmonic oscillator.(adsbygoogle = window.adsbygoogle || []).push({});

Griffiths solves the Schrodinger equation using ladder operators, and he then says that there must be a "lowest rung," or [tex]\psi_{0}[/tex], such that a_[tex]\psi_{0}[/tex] = 0. I'm guessing this also means that E = 0 for a_[tex]\psi_{0}[/tex], which is why it wouldn't be allowable.

Because a_[tex]\psi_{0}[/tex] is (mathematically, at least) a solution to the Schrodinger equation, it corresponds to the energy ([tex]E_{0}[/tex] - [tex]\hbar\omega[/tex]), which equals zero. Doesn't this mean that [tex]E_{0}[/tex] = [tex]\hbar\omega[/tex]?

But then this conflicts with Griffith's statement that [tex]E_{0}[/tex] = [tex]\frac{1}{2}\hbar\omega[/tex]. HELP!

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# Harmonic Oscillator

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