Fewpal
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+2 votes
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The Schr¨odinger equation has two ‘forms’, one in which time explicitly appears, and so describes how the wave function of a particle will evolve in time. In general, the wave function behaves like a wave, and so the equation is often referred to as the time dependent Schr¨odinger wave equation. The other is the equation in which the time dependence has been ‘removed’ and hence is known as the time independent Schr¨odinger equation and is found to describe, amongst other things, what the allowed energies are of the particle. These are not two separate, independent equations – the time independent equation can be derived readily from the time dependent equation (except if the potential is time dependent, a development we will not be discussing here). In the following we will describe how the first, time dependent equation can be ‘derived’, and in then how the second follows from the first.

+2 votes
by (2.4k points)

this the equation

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