What is Schrödinger equation with potential terms?

The Schrödinger equation with potential terms is like a recipe that tells us how things move and change when they’re affected by different kinds of forces.

Imagine you're playing with a ball on a hill. If the hill is flat, it’s easy to predict where the ball will go, just roll down! But if there are bumps or valleys in the way, those can change its path. In this case, each bump or valley acts like an obstacle or a helper, and we call them potential terms.

Without any bumps or valleys (no potential terms), it’s simple, the ball just moves smoothly. But when there are hills or valleys around, it's as if the ball is being pushed or pulled by invisible hands.

These potential terms can be like:

• A hill that makes the ball slow down
• A valley that speeds it up
• An invisible wall that stops it

The Schrödinger equation with potential terms helps scientists understand how tiny particles, like electrons in an atom, move and behave when they're affected by these kinds of invisible forces, just like our ball on a bumpy hill.