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

Time-independent Schrödinger equationEdit

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