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I am trying to self learn a little bit of quantum mechanics in order to describe the magnetic resonance phenomenon. I am following Griffiths book and i am understanding most of it.

Now, there is a particular thing that is bogging me.

The Schrodinger equation can be easily solved by separation of variables if the potential does not depend on time, which i understand as:

[itex]\frac{\partial V(x,t)}{\partial t}=0[/itex]

in other words it can simply be

[itex]V(x,t)\rightarrow V(x)[/itex]

Now i can think of a many motions where the potential is constant at any given position in time. For instance the Harmonic oscillator or an electron orbiting.

Now i cant imagine in my naive approach, a possible scenario where the potential changes with time without changing the position of a particle.

Is there any easy explanation for that?

Ty in advance