Unformatted text preview: H = 1 2 m p 2 + 1 2 mω 2 x 2 . a) Show that the function φ = Ae-αx 2 is an eigenfunction of H for a particular α . What must α be? What are its units? b) What is the eigenvalue of H that corresponds to φ ? c) Show that xφ is also an eigenfunction of H . What is its eigenvalue? d) Compute Δ x and Δ p for the state in c). Compare the Δ x Δ p product with that of φ . (Hint: Note that some of the same integrals appear multiple times here. Also, be careful about normalization.)...
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- Spring '09
- Work, Worth1000, 2m, short answer problem