Quantum Mathematics in Relation to Quantum Physics
Date Written: August 30, 2013
In Quantum Mathematics, the evolution of the states of a dynamical system is deterministic. For instance, given time t, the states of the system are completely determined by the dynamical state at the initial time t. Suppose, a question like x^2-2x+2=0 is solved using completing square method, you will realize that finding the square root of √-1 is impossible; hence, this is a complex number. Additionally, solving a problem of finding a formula for a power of a square matrix A requires the construction of matrices which transform A into diagonal matrix. It is done with any square matrix A, associating homogeneous linear equations Ax=0. Such set of equations will only have non-trivial solutions set if det A=0. These are defined as eigenvalues and eigenvectors. To understand quantum mathematics, one must understand the mathematical models and theories to gain insight for employing physics and mechanics in it. Some mathematicians have solved quantum problems using philosophical approaches which is favorable to them; the strategy I have used is to treat finitely dimensional operators and numbers in some detail and to indicate in general terms how the sane ideas are applied in the physics case.