Operators and Matrices

WU Jun-fang, Zhang Chun-Min

Aim The Hamiltonian is transformed from Pauli matrices to Hubbard operators. Method we use the unity and orthogonal of Hubbard operators to give the transforming formula of Pauli matrices and Hubbard operators, by using these transforming formula we realize the change from Pauli matrices to Hubbard operators. Result we get the Hamiltonian expressed by Hubbard operators of the spin-ladder model. Conclusion We use the example to realize the transform between Hubbard operators and Pauli matrices.

WU Jun-fang

Aiming at the transformation of Hamiltonian from Pauli matrices to Hubbard operators, the authors use the unity and orthogonal of Hubbard operators to give the transforming formula of Pauli matrices and Hubbard operators, by which, they realize the change from Pauli matrices to Hubbard operators.The result has been obtained that the Hamiltonian expressed by Hubbard operators of the spin-ladder model.

Brian L. Silver

Sadri Hassani

Z. Ficek

This chapter illustrates how one can obtain a matrix representation of a state vector, an operator, and an eigenvalue equation in a basis of orthonormal states. It helps to learn that matrix representations are very useful in calculations of the properties of operators, because algebra of matrices is very simple and completely developed. Readers familiar with the algebra of matrices agree that mathematical operations on matrices such as multiplication by a scalar, addition, subtraction, multiplication and diagonalization are simple and easy to perform. In fact, the application of the algebra of matrices to quantum physics results from the direct relations between operators and matrices that any mathematical relation that holds between operators also holds between the corresponding matrices. The eigenvalues and eigenvectors of the matrix representing a given operator  in the basis of orthonormal states are the same as the eigenvalues and eigenvectors of Â.