Page 13 - 71 the abc of dft_opt
P. 13

1.6. QUESTIONS                                                      25     26                                                CHAPTER 1. INTRODUCTION
       Extra exercises

                                                                       2
        1. For a δ-function potential, v(x) = −Zδ(x), the ground-state kinetic energy is Z /2 and
          the density is Z exp(−2Zx). Before calculating the local approximation, first guess if it
          will be an overestimate or an underestimate, and by how much.
                                           2
                                                                      2
                                       2
        2. Another famous example is v(x) = −a sech (ax), with ground-state energy −a /2 and
                    2
          density a sech (ax)/2. Repeat above problem.
   8   9   10   11   12   13   14   15   16   17   18