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The Schrodinger equation is going to express how quantum mechanical systems change with time. This equation, will describe the behavior of a quantum mechanical wave. The Schrodinger equation essentially defines two properties of the quantum system:
It defines the system's permitted stationary states. Schrodinger proposed that electrons could only have orbits where a whole number of the electron's associated waves can fit. If it lay in between these states, where the orbits could contain a fractional number of wavelengths than it was not allowed.
It describes how the state of a quantum mechanical system changes with time.
The wave is described by a function called a wave function. According to Erwin Schrodinger, the purpose of the wave function was to be used to predict the probability of certain results being measured. It did not only apply to electrons, however, to all subatomic particles. This was not the description of the motion of particles, as in Newtonian mechanics. However, this was wave mechanics: a description of the propagation of waves.
In quantum mechanics, we are only able to make predictions about the probability of certain particle behavior. This is the way nature behaves at the subatomic level: it is probabilistic. An electron's associated probability wave will determine the location that that electron will most likely be located.
Erwin Schrodinger, an Austrian physicist, in 1926, publishes his Schrodinger equation, which describes how quantum mechanical systems change in time.
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