Matrix Mechanics
An algebraic formulation of quantum mechanics created by Werner Heisenberg in 1925 expressing physical observables as infinite-dimensional matrices.
Governing formula
p̂ q̂ - q̂ p̂ = -i ℏ I, Ĥ = H(q̂, p̂)
SI unit
Matrix Operator Algebra
In depth
Matrix mechanics describes quantum transitions without relying on classical trajectories. Observables are represented by Hermitian matrices whose non-commutativity ([x̂, p̂] = i ℏ I) directly yields the quantum uncertainty principle.
Examples in the real world
Solving quantum harmonic oscillator energy levels using creation and annihilation ladder matrix operators.