============================================================= --> This small program will print out the possible many-body states for a given electronic configuration --> The obtained states of single Slater determinants will be used as a Hilbert space for several operators. ============================================================= Calculating all possible Slater determinants for a shell with angular momentum 1 and a filling of 1 electrons ======================== O U T P U T ======================== A shell with l= 1 and a filling of 1 electrons has Binomial(6 1) = 6 possible single Slater determinants --> List of possible single Slater determinants which span the basis for all many body states: 1 |100000> 2 |010000> 3 |001000> 4 |000100> 5 |000010> 6 |000001> ============================================================= The Sz operator on a basis Single slater determinants for a shell with l = 1 and a filling of 1 electrons is: 1 |100000> -0.50 0.00 0.00 0.00 0.00 0.00 2 |010000> 0.00 0.50 0.00 0.00 0.00 0.00 3 |001000> 0.00 0.00 -0.50 0.00 0.00 0.00 4 |000100> 0.00 0.00 0.00 0.50 0.00 0.00 5 |000010> 0.00 0.00 0.00 0.00 -0.50 0.00 6 |000001> 0.00 0.00 0.00 0.00 0.00 0.50 ============================================================= The Lz operator on a basis Single slater determinants for a shell with l = 1 and a filling of 1 electrons is: 1 |100000> -1.00 0.00 0.00 0.00 0.00 0.00 2 |010000> 0.00 -1.00 0.00 0.00 0.00 0.00 3 |001000> 0.00 0.00 0.00 0.00 0.00 0.00 4 |000100> 0.00 0.00 0.00 0.00 0.00 0.00 5 |000010> 0.00 0.00 0.00 0.00 1.00 0.00 6 |000001> 0.00 0.00 0.00 0.00 0.00 1.00 ============================================================= The S^2 operator on a basis Single slater determinants for a shell with l = 1 and a filling of 1 electrons is: 1 |100000> 0.75 0.00 0.00 0.00 0.00 0.00 2 |010000> 0.00 0.75 0.00 0.00 0.00 0.00 3 |001000> 0.00 0.00 0.75 0.00 0.00 0.00 4 |000100> 0.00 0.00 0.00 0.75 0.00 0.00 5 |000010> 0.00 0.00 0.00 0.00 0.75 0.00 6 |000001> 0.00 0.00 0.00 0.00 0.00 0.75 ============================================================= The L^2 operator on a basis Single slater determinants for a shell with l = 1 and a filling of 1 electrons is: 1 |100000> 2.00 0.00 0.00 0.00 0.00 0.00 2 |010000> 0.00 2.00 0.00 0.00 0.00 0.00 3 |001000> 0.00 0.00 2.00 0.00 0.00 0.00 4 |000100> 0.00 0.00 0.00 2.00 0.00 0.00 5 |000010> 0.00 0.00 0.00 0.00 2.00 0.00 6 |000001> 0.00 0.00 0.00 0.00 0.00 2.00 ============================================================= The Coulomb operator for a shell with l = 1 is given by 2 different operators depending on the angular momentum of the expansion of 1/|r1-r2| in spherical Harmonics ============================================================= F[0] 1 |100000> 0.00 0.00 0.00 0.00 0.00 0.00 2 |010000> 0.00 0.00 0.00 0.00 0.00 0.00 3 |001000> 0.00 0.00 0.00 0.00 0.00 0.00 4 |000100> 0.00 0.00 0.00 0.00 0.00 0.00 5 |000010> 0.00 0.00 0.00 0.00 0.00 0.00 6 |000001> 0.00 0.00 0.00 0.00 0.00 0.00 ============================================================= F[2] 1 |100000> 0.00 0.00 0.00 0.00 0.00 0.00 2 |010000> 0.00 0.00 0.00 0.00 0.00 0.00 3 |001000> 0.00 0.00 0.00 0.00 0.00 0.00 4 |000100> 0.00 0.00 0.00 0.00 0.00 0.00 5 |000010> 0.00 0.00 0.00 0.00 0.00 0.00 6 |000001> 0.00 0.00 0.00 0.00 0.00 0.00 ============================================================= Timing results Total_time | NumberOfRuns | Running | Name 0:00:00 | 1 | 0 | Create Determinants 0:00:00 | 1 | 0 | Create operators in second quantization 0:00:00 | 1 | 0 | Create operators in matrix form