Show that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator 1. Compute T(hat)*psi 2. Compute Vhat* psi - assume V operator is 1/2w^2x^2 3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true 4. From cancellation find a 5. insert back a to Schrodinger eq above and find E
Show that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator 1. Compute T(hat)*psi 2. Compute Vhat* psi - assume V operator is 1/2w^2x^2 3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true 4. From cancellation find a 5. insert back a to Schrodinger eq above and find E
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Show that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator
1. Compute T(hat)*psi
2. Compute Vhat* psi - assume V operator is 1/2w^2x^2
3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true
4. From cancellation find a
5. insert back a to Schrodinger eq above and find E
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