text: The Hamiltonian describing a spinor condensate is most frequently written using the language of 
  second quantization.   Here the field operator
  creates a boson in Zeeman level  at position .  These
  operators satisfy bosonic commutation relations:
  The free (non-interacting) part of the Hamiltonian is
  where  denotes the mass of the constituent particles and 
    is an external potential.
  For a spin-one spinor condensate, the interaction Hamiltonian is
  In this expression, 
  is the operator corresponding to the density, 
  is the local spin operator (
  is a vector composed of the spin-one matrices),
  and :: denotes normal ordering.   The parameters 
  can be expressed in terms of the s-wave scattering lengths of the constituent particles.
  Higher spin versions of the
  interaction Hamiltonian are slightly more involved, but 
  can generally be expressed by using Clebsch–Gordan coefficients.
  The full Hamiltonian then is .