Here is the equation saying what an electron does in a hydrogen atom:

It's called Schrödinger's equation.

ψ is the wavefunction of the electron, depending on time and place.

ℏ is Planck's constant h divided by 2π.

m is the electron's mass.

e is the electron's charge.

r is the distance from the proton.

i is the square root of -1.