# This Quantum World/Implications and applications/Time independent Schrödinger equation

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## Time-independent Schrödinger equation[edit]

If the potential V does not depend on time, then the Schrödinger equation has solutions that are products of a time-independent function and a time-dependent phase factor :

Because the probability density is independent of time, these solutions are called *stationary*.

Plug into

to find that satisfies the time-independent Schrödinger equation