# Time development

As **time evolution** is defined as the state change of a mostly physical system represented by the progression of time is effected. The mathematical description of the development over time is usually described with the help of differential equations, so-called equations of motion . In classical mechanics these are, for example, the Hamilton equations or two of the four Maxwell equations , in quantum mechanics it is the time-dependent Schrödinger equation . The time does not have to be a constant quantity here , it can alsobe discreet or finite .

The concept of time evolution can also be applied to non-physical systems for which the concept of a state in which they are located can be well defined ( stateful systems). An example of such a system with a discrete time is a Turing machine , in which the overall condition is given by the status of the control unit and the tapes as well as the position of the read / write head. The time development is determined by the program.

Stateful systems can often be described both by their state and by the values of the observables . In such systems, the time evolution can also refer to changes in the observable values. This is particularly true of quantum mechanics, in which the Schrödinger picture and the Heisenberg picture are (almost) equivalent descriptions of the development of time.