Quantum mechanics explain how electrons have both a particle-like and a wave-like characteristics
The Schroedinger equation describes the wavefunction of a particle:
is the wavefunction, m is the mass of the particle, his Plancks constant, V is the potential field in which the particle is moving
The equation for a collection of particles (like a molecule) is very similar. would be a function of the coordinates of all the particles in the system as well as time t.
Energy and other properties of the particle can be obtained by solving the equation for subject to the appropriate boundary conditions. Many different wavefunctions are solutions to it, corresponding to different stationary states.