There is no indeterminacy in the time evolution of a quantum system. Indeterminacy appears only when a physical quantity is measured, the state function then undergoing an unpredictable modification. Such a superposition can be written as . A plane wave, whose modulus is constant throughout all space, is not square-integrable, therefore, rigorously, it cannot represent a physical state of the particle. On the other hand, the superposition of plane waves can be square-integrable.
Analytical solution exists only for some oversimplified cases.
This gives the time rate of change of the state function at the initial time instant t 0 . By choosing short time intervals and close values of the x coordinate the method provides a good approximation of the evolution of the state function. To get the evolution of the wave function by the outlined method in two or three dimensions is rather hopeless, mainly because of computational time limitations. These limitations are largely removed by an efficient numerical technique based on splitting of the evolution operator and Fourier transform technique. Unitarity expresses the conservation of probability.