The matrix rotating an operator on the basis of spherical harmonics with alternating spin to a basis of kubic harmonics with alternating spin for a p orbital is: { { 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 , 0 } , { 0 , 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 } , { (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 } , { 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) } , { 0 , 0 , 1 , 0 , 0 , 0 } , { 0 , 0 , 0 , 1 , 0 , 0 } } The operator adding a potential to the px orbital on a basis of spherical harmonics is: Operator: Opp px QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 2 (largest number of product of lader operators) NFermionic modes = 6 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 8 (number of operators of length 2) C 0 A 0 | 4.999999999999999E-01 C 1 A 1 | 4.999999999999999E-01 C 4 A 4 | 4.999999999999999E-01 C 5 A 5 | 4.999999999999999E-01 C 4 A 0 | -5.000000000000000E-01 C 5 A 1 | -5.000000000000000E-01 C 0 A 4 | -5.000000000000000E-01 C 1 A 5 | -5.000000000000000E-01 The operator adding a potential to the px orbital on a basis of kubic harmonics is: Operator: Opp px QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 2 (largest number of product of lader operators) NFermionic modes = 6 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 2 (number of operators of length 2) C 0 A 0 | 1.000000000000000E+00 C 1 A 1 | 1.000000000000000E+00 The operator adding a potential to the py orbital on a basis of spherical harmonics is: Operator: Opp py QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 2 (largest number of product of lader operators) NFermionic modes = 6 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 8 (number of operators of length 2) C 0 A 0 | 4.999999999999999E-01 C 1 A 1 | 4.999999999999999E-01 C 4 A 4 | 4.999999999999999E-01 C 5 A 5 | 4.999999999999999E-01 C 4 A 0 | 5.000000000000000E-01 C 5 A 1 | 5.000000000000000E-01 C 0 A 4 | 5.000000000000000E-01 C 1 A 5 | 5.000000000000000E-01 The operator adding a potential to the py orbital on a basis of kubic harmonics is: Operator: Opp py QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 2 (largest number of product of lader operators) NFermionic modes = 6 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 2 (number of operators of length 2) C 2 A 2 | 1.000000000000000E+00 C 3 A 3 | 1.000000000000000E+00 The operator adding a potential to the pz orbital on a basis of spherical harmonics is: Operator: Opp pz QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 2 (largest number of product of lader operators) NFermionic modes = 6 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 2 (number of operators of length 2) C 2 A 2 | 9.999999999999999E-01 C 3 A 3 | 9.999999999999999E-01 The operator adding a potential to the pz orbital on a basis of kubic harmonics is: Operator: Opp pz QComplex = 0 (Real==0 or Complex==1 or Mixed==2) MaxLength = 2 (largest number of product of lader operators) NFermionic modes = 6 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis) NBosonic modes = 0 (Number of bosonic modes (phonon modes, ...) in the one particle basis) Operator of Length 2 QComplex = 0 (Real==0 or Complex==1) N = 2 (number of operators of length 2) C 4 A 4 | 9.999999999999999E-01 C 5 A 5 | 9.999999999999999E-01 The px orbital with spin down on a basis of spherical harmonics is: WaveFunction: Wave Function QComplex = 0 (Real==0 or Complex==1) N = 2 (Number of basis functions used to discribe psi) NFermionic modes = 6 (Number of fermions in the one particle basis) NBosonic modes = 0 (Number of bosons in the one particle basis) # pre-factor Determinant 1 7.071067811865E-01 100000 2 -7.071067811865E-01 000010 The px orbital with spin down on a basis of kubic harmonics is: WaveFunction: Wave Function QComplex = 0 (Real==0 or Complex==1) N = 1 (Number of basis functions used to discribe psi) NFermionic modes = 6 (Number of fermions in the one particle basis) NBosonic modes = 0 (Number of bosons in the one particle basis) # pre-factor Determinant 1 1.000000000000E+00 100000 The py orbital with spin down on a basis of spherical harmonics is: WaveFunction: Wave Function QComplex = 1 (Real==0 or Complex==1) N = 2 (Number of basis functions used to discribe psi) NFermionic modes = 6 (Number of fermions in the one particle basis) NBosonic modes = 0 (Number of bosons in the one particle basis) # pre-factor +I pre-factor Determinant 1 0.000000000000E+00 7.071067811865E-01 100000 2 0.000000000000E+00 7.071067811865E-01 000010 The py orbital with spin down on a basis of kubic harmonics is: WaveFunction: Wave Function QComplex = 0 (Real==0 or Complex==1) N = 1 (Number of basis functions used to discribe psi) NFermionic modes = 6 (Number of fermions in the one particle basis) NBosonic modes = 0 (Number of bosons in the one particle basis) # pre-factor Determinant 1 1.000000000000E+00 001000 The pz orbital with spin down on a basis of spherical harmonics is: WaveFunction: Wave Function QComplex = 0 (Real==0 or Complex==1) N = 1 (Number of basis functions used to discribe psi) NFermionic modes = 6 (Number of fermions in the one particle basis) NBosonic modes = 0 (Number of bosons in the one particle basis) # pre-factor Determinant 1 1.000000000000E+00 001000 The pz orbital with spin down on a basis of kubic harmonics is: WaveFunction: Wave Function QComplex = 0 (Real==0 or Complex==1) N = 1 (Number of basis functions used to discribe psi) NFermionic modes = 6 (Number of fermions in the one particle basis) NBosonic modes = 0 (Number of bosons in the one particle basis) # pre-factor Determinant 1 1.000000000000E+00 000010 Counting the px orbital on a basis of spherical harmonics: 1 Counting the px orbital on a basis of kubic harmonics: 1 Counting the py orbital on a basis of spherical harmonics: 1 Counting the py orbital on a basis of kubic harmonics: 1 Counting the pz orbital on a basis of spherical harmonics: 1 Counting the pz orbital on a basis of kubic harmonics: 1