Problem Set 4

Problem Set 4 - intermediate value of L . 2. Shankar,...

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PHYSICS 230 – PROBLEM SET 4 1. Review the bound state problem for a single delta function potential. Then find the bound states for a potential consisting of two delta func- tions separated by a distance L . V ( x ) = - λ ( δ ( x + L/ 2) + δ ( x - L/ 2)) Show that this reduces to the correct limits as L → ∞ and L 0. Give a formula for the energy splitting between the bound states valid for large but finite L . Show that something interesting happens at an
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Unformatted text preview: intermediate value of L . 2. Shankar, problem 7.4.2 and problem 7.4.5 . 3. Evaluate < | x 6 | > for the harmonic oscillator using raising and lower-ing operator techniques and directly using the ground state wavefunc-tion. This gives a hint of the connection between gaussian integrals and Feynman diagrams....
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