Chemistry 3730 assignment 6 solutions

1. As always, we begin by defining the wavefunction:
   

   > psi := x -> A*exp(-a*x^2);

   

   
   

   Normalization requires .
   

   > int(psi(x)^2,x=-infinity..infinity);

   Definite integration: Can't determine if the integral is convergent.
   Need to know the sign of --> 2*a
   Will now try indefinite integration and then take limits.

   

   
   

   Maple wants to know the sign of a.
   

   > assume(a>0);
   > int(psi(x)^2,x=-infinity..infinity);

   

   
   

   This integral must equal 1 so

   

2. 1. must be at least

      

      The momentum and kinetic energy are related by

      

      Therefore

      

   2. This is an opportunity to use the error propagation formulas you learned in analytical chemistry. Since ,

      

      or about 0.03% of the kinetic energy.