Now let's treat the simple pendulum quantum mechanically (a) In the small x limit, construct a fo...
Now let's treat the simple pendulum quantum mechanically (a) In the small x limit, construct a formula for the energy levels. (b) If x isn't so small, we should include a second term (proportional to x) in the expansion of the potential energy function. Treating this second term as a perturbation, set up an expression for the correction it provides to the zero-point energy and determine the sign of this correction (i.e., + or -). (c) Explain how your result in (b) could also follow from a heuristic (i.e., "stylish hand- waving") uncertainty principle argument.
Now let's treat the simple pendulum quantum mechanically (a) In the small x limit, construct a formula for the energy levels. (b) If x isn't so small, we should include a second term (proportional to x) in the expansion of the potential energy function. Treating this second term as a perturbation, set up an expression for the correction it provides to the zero-point energy and determine the sign of this correction (i.e., + or -). (c) Explain how your result in (b) could also follow from a heuristic (i.e., "stylish hand- waving") uncertainty principle argument.