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|. , and so hv i = 2b . The expectation value of the double derivative e 2bx2 dx = a2r . Therefore, the hamiltonian expectation value reads hhi = Minimizing with respect to b, we obtain b 3/2 b3/2 = For spherically symmetrical potentials we can apply the wkb approximation to the radial part. In the case l = 0 the answer is. 1 (8) 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) (9) (for constants v0 and a). Show that the spacing between the levels is independent of mass. E = v0 ln r0 a de nes r0.
