[3] Specifically, as a study of dynamics, this field investigates how quantum mechanical observables change over time.
Recently, mathematicians in the field have studied irreversible quantum mechanical systems on von Neumann algebras.
[4] Equations to describe quantum systems can be seen as equivalent to that of classical dynamics on a macroscopic scale, except for the important detail that the variables don't follow the commutative laws of multiplication.
[5] Hence, as a fundamental principle, these variables are instead described as "q-numbers", conventionally represented by operators or Hermitian matrices on a Hilbert space.
In this realm of quantum systems, the equation of motion governing dynamics heavily relies on the Hamiltonian, also known as the total energy.