Question

(100pts) For full credit show ALL work. The variational method is commonly used in various guises in physics to determine the quantum ground states of solids. One of the properties of ground states is that they are local minima with respect to some parameter (in this case μ ) thus they are the "lowest energy state" one can obtain as a function of this parameter. Consider a "hydrogen like" atom. Assume the electron is n the (r)-Be-u state, where B is a normalization constant and μ is a constant to be determined by energy minimization. In the calculations below assume s--20.0eP,ー 7.62eV«A.e. = 14.40eT.4, here eV = electron volt (energy) and A-1 Angstrom = 1.0x10-10 m. 2 1.b) (20 pts) Now assume that the Hamiltonian operator (a quantum expression used to calculate the total energy of the p, (r) electron ) in spherical coordinates is given by Define the total energy of the p, (r) electron to be Take a variation of the total energy with respect to fu and set it equal to zero To obtain the value of μ . To obtain this value assume Using these values the constant μ will have the units of inverse Angstroms.

Answer 1

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m c