// Alex Fernez, 2018 Simply to explain the contents of this folder: Eigen contains the linear algebra functionality needed to solve the eigenvalue equation for the Matrix Hamiltonian that is set up according to the Wu, Lee, Thomas, and Young paper in Matrix_Hamiltonian.cpp. The header file contains the class definitions and the functionality that is available to the user, with some comments to indicate possibly non-obvious things. To illustrate an expected use of the Matrix Hamiltonian implementation, see the code in the Matrix_Hamiltonian.cpp main() function that is commented out. The user is asked to provide a set of bare states, a set of two-particle-channels for a given scattering reaction, and then set the number of momenta they want to consider and the length of the finite box to consider the reaction within. After this, everything is taken care of when the user creates a Hamiltonian object; all elements of the Hamiltonian are automatically set and the eigenvalues and eigenvectors are computed and stored in the Hamiltonian object. In order to see the results for the given parameters, functions are defined within the header file that allow the user to see the contents of the Hamiltonian object. Further, the Hamiltonian constructor also allows the possibility of inputting two user-defined potentials as the 5th and 6th parameters- for the vertex interaction and two-particle two-particle interaction, respectively. Hopefully, this will ease the process of trying to fit the model and verify the constants that the paper proposes. If these values are not used, currently the default potentials are set to be used for the pipi scattering, 1b2c reaction considered in the paper by Wu, Lee, Thomas, and Young. Hopefully also to ease the process of fitting the model proposed by the paper: when the user creates a Hamiltonian object, they have the option to "set" (or, really, reset) n, L, the set of bare states used, the set of two particle channels used, the vertex interaction potential used, or the two-particle two-particle interaction used. When one of these "set" functions is called, everything in the Hamiltonian- its element, eigenvalues, etc- is automatically recalculated. Without knowing exactly what process is to be used for fitting the model, this is all the functionality I could think of adding to the program. In order to consider more than just the pipi scattering that the paper explores, the user will just have to define new g and v potential functions. Everything else in the program should work if these functions are provided (assuming they are created with the right forms-- see the typedefs in the header file defining g_func and v_func types). Possible future considerations: In order to calculate the energy associated with what the Australians' papers call discrete states, in Matrix_Hamiltonian.cpp I have defined a discrete state class. This class's fields include the masses of the two particles used to define the state and the magnitude of the momentum of each particle (quantized since we are on a lattice, equal and opposite since we are working in the CM frame, and stored in terms of a variable n, where k=sqrt(n)*2pi/L). Then, when I define the functions that return the energies associated with the discrete state, I multiply the value of k by h_bar*c (so that it equals pc) in order that E = sqrt((mc^2)^2 + (pc)^2) is correctly satisfied. Though, I am not sure if this is right. The paper works entirely in natural units (h_bar=c=1), but I think that in order to get a correct value for E (in MeV) I need to perform this multiplication. It is important to change this in the implementation if this is not the correct thing to do, however.