Sean Vig's 2011 GSOC Project

Developing Wigner-3nj Symbols in SymPy

Developing Coupled/uncoupled States and Operators

Most of this last week was spent developing coupled and uncoupled states, beginning to develop how operators will act on these states and writing tests to ensure the code returns the desired result. This week I finished up writing the code for expressing states, and the logic for rewriting from one to the other and back. In addition to this, I implemented the tests which are used for these rewrites. This mostly finishes up the logic for the coupled/uncoupled states, there is still the represent logic which may need to be implemented, tho this will take some looking into to determine what is appropriate and necessary to implement.

For the operators, using the qapply logic already in place, I have begun to implement how operators act on coupled and uncoupled states. I have thus far only implemented logic for coupled operators, that is, for example $J_z = J_{z_1} + J_{z_2}$ ($=J_{z_1} \otimes 1 + 1 \otimes J_{z_2}$ in an uncoupled representation). In addition to defining how uncoupled product states are acted upon by spin operators, I have expanded those already implemented methods to act on arbitrary states, as they had only previously been defined in how they act on JzKet’s. This was done by defining a basis, such that, with the now improved rewrite logic, any state can be rewritten into an appropriate basis for the state and the state in then acted upon by the operator. I have begun to implement the tests that ensure the implemented logic is valid in all cases, both numerical and symbolic, tho this is still a work in progress.

The focus for this next week will be continuing the development of the spin operators, hopefully getting to working with uncoupled spin operators, i.e. operators given in a tensor product to only act on one of the uncoulped states, and developing the tests necessary to the implementation of these states. If I can complete this, I will be closing in on the completion of the coupling of two spin spaces.