Matrix mechanics

                                 Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.

Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps occur. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, and is the basis of Dirac's bra-ket notation for the wave function.

In some contrast to the wave formulation, it produces spectra of energy operators by purely algebraic, ladder operator, methods. Relying on these methods, Pauli derived the Hydrogen atom spectrum in 1926,  before the development of wave mechanics.