Homework 2#
This homework is due on Tuesday January 23rd. You should submit a PDF of your solutions on myCourses.
(a) Apply the Heisenberg uncertainty principle to estimate the ground state energy and wave-function spread of the harmonic oscillator, using arguments similar to those given in class for the hydrogen atom. Explain whether you get the answer you expect or not.
(b) Consider a 1D finite square well with depth \(V_0\) and width \(a\). Estimate the minimal kinetic energy of a particle with mass \(m\) confined to a distance \(a\). For what values of \(a\) does the kinetic energy exceed \(V_0\)? How do you reconcile your answer with the fact that 1D finite square wells always have a bound state, for all values of \(a\), \(m\), and \(V_0\)?Townsend 9.5.
Townsend 9.7.
Townsend 9.8.
Hint for Townsend 9.7: the cross product of two vectors is given in terms of \(\epsilon_{ijk}\) by \((\vec{A}\times\vec{B})_i = \epsilon_{ijk} A_jB_k\).
Hint for the last part of 1(b): Draw a rough sketch of the wavefunction you expect for the bound state.