PHYSICS 137B Study Guide - Midterm Guide: Morse Potential, Cubic Function
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Physics 137 b spring 2012 - midterm 1. For z < 0, we assume v (z) = + , i. e. , the particle has zero probability of getting to z < 0. As you know, the normalized wave functions for this potential are n(x) = p2/a sin(n x/a) and the energy levels are en = (n h)2/(2ma2). Now consider a small modi cation of the potential by v (x) = v0 sin( x/a). Calculate the energy level shift in rst order perturbation theory: the potential between two atoms forming a molecule can be approximated by a morse potential u (r) = de(e 2a(r re) 1: (5 points) consider oscillations of small amplitude around the minimum of the potential. The masses of the atoms are m1 and m2, respectively. Treat the di erence of u (r) and the harmonic approximation in rst-order perturbation theory.
