Solutions for the Equation of Motion

Günther Ludwig

Henryk Gzyl

The authors show that when the Weyl correspondence is employed to associate operators to functions defined on phase space, then for Hamiltonians of the form K(rho) + V(q), the solution to the Heisenberg equations of motion can be obtained from the classical solution of the Hamilton equations of motion.

Dawit Hiluf Hailu

In this paper we introduce the use of Sylvester's formula for systems with degenerate eigenvalues in relation to obtaining their analytical solutions. To appreciate the use we include two other forms of analytical solutions namely adiabatic and Magnus approximations. In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the evolution over time of a physical system in which quantum effects, such as wave--particle duality, are significant. The equation is a mathematical formulation for studying quantum mechanical systems. Just like Newtons's laws govern the motion of objects, Schrödinger equations of motion also govern the motion of quantum objects. Unlike the classical motion of objects the equation of motions of quantum phenomenon deals with the likelihood of the trajectories.

Umberto Lombardo, G. Giuliani, Yifei Niu

Hernan C. Praddaude

Michael G Cottam, Zahra Haghshenasfard