Tz

\subsection{$T_z$} The z component of $\vec{T}$ is defined as: \begin{equation} T_z = S_z - 3 z\left(x S_x + y S_y + z S_z\right)/r^2. \end{equation} The equivalent operator in Quanty is created by:

Example.Quanty

OppTz = NewOperator("Tz", NF, IndexUp, IndexDn)

The operator can alternatively be created with the following function:

Example.Quanty

function Tz(indexup, indexdn, NF)
  if #indexup ~= #indexdn then
    error("Length of index up must be equal to length of index dn and equal to 2l+1 in Tz")
  end
  local l=(#indexup-1)/2
  if not IntegerQ(l) then
    error("Length of index must be equal to 2l+1 in Tz")
  end
  local function Sx(m1,m2) 
    return NewOperator("Number",NF,{indexup[m1+l+1],indexdn[m1+l+1]},
                       {indexdn[m2+l+1],indexup[m2+l+1]},{1/2,1/2})
  end
  local function Sy(m1,m2) 
    return NewOperator("Number",NF,{indexup[m1+l+1],indexdn[m1+l+1]},
                       {indexdn[m2+l+1],indexup[m2+l+1]},{-I/2,I/2})
  end
  local function Sz(m1,m2) 
    return NewOperator("Number",NF,{indexup[m1+l+1],indexdn[m1+l+1]},
                       {indexup[m2+l+1],indexdn[m2+l+1]},{1/2,-1/2})
  end
  local opp = 0 * NewOperator("Number",NF,0,0)
  for m1 = -l,l do
    for m2 = -l,l do
      opp = opp -2 * (           SlaterCoefficientC({l,m1},{2, 0},{l,m2})
                     )*Sz(m1,m2)
                -    ( sqrt(3/2)*SlaterCoefficientC({l,m1},{2,-1},{l,m2})
                      -sqrt(3/2)*SlaterCoefficientC({l,m1},{2, 1},{l,m2})
                     )*Sx(m1,m2)
                -I * ( sqrt(3/2)*SlaterCoefficientC({l,m1},{2,-1},{l,m2})
                      +sqrt(3/2)*SlaterCoefficientC({l,m1},{2, 1},{l,m2})
                     )*Sy(m1,m2)
    end
  end
  opp.Chop()
  opp.Name="Tz"
  return opp
end