Use the Ritz variational method for the harmonic oscillator, with trial wave functions (psi_{1}(x)=) (e^{-y^{2} / 2},

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Use the Ritz variational method for the harmonic oscillator, with trial wave functions \(\psi_{1}(x)=\) \(e^{-y^{2} / 2}, \psi_{2}(x)=e^{-y^{2}}, \psi_{3}(x)=e^{-2 y^{2}}\), where \(y=x \sqrt{m \omega / \hbar}\), in order to find the best approximation to the ground state energy.

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