PHYSICS 137B Study Guide - Midterm Guide: Gyromagnetic Ratio
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Use a gaussian trial function to obtain the lowest upper bound you can on the ground state energy of the linear potential v (x) = |x|. For spherically symmetrical potentials we can apply the wkb approximation to the radial part. In the case l = 0 the answer is. 0 p(r)dr = (n 1/4) , (2) where r0 is the turning point (in e ect, we treat r = 0 as an in nite wall). Exploit this formula to estimate the allowed energies of a particle in the logarithmic potential. V (r) = v0 ln(r/a) (3) (for constants v0 and a). Show that the spacing between the levels is independent of mass. Consider an electrically neutral body that can rotate about a xed axis, with moment of inertia i. Correspondingly, we add a new term to our hamiltonian, of the form. H = s l where is small and s is the electron spin operator.
