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 .