The Schrodinger equation was formulated in 1926 by Austrian physicist Erwin Schrodinger. Used in physics, specifically quantum mechanics, it is an equation that describes how the quantum state of a physical system changes in time.
In the standard interpretation of quantum mechanics, the quantum state, also called a wavefunction or state vector, is the most complete description that can be given to a physical system. Solutions to Schrodinger's equation describe not only molecular, atomic and subatomic systems, but also macroscopic systems, possibly even the whole universe.
The most general form is the time-dependent Schrodinger equation, which gives a description of a system evolving with time. For systems in a stationary state (i.e., where the Hamiltonian is not explicitly dependent on time), the time-independent Schrodinger equation is sufficient. Approximate solutions to the time-independent Schrodinger equation are commonly used to calculate the energy levels and other properties of atoms and molecules.
Schrodinger's equation can be mathematically transformed into Werner Heisenberg's matrix mechanics, and into Richard Feynman's path integral formulation. The Schrodinger equation describes time in a way that is inconvenient for relativistic theories, a problem which is not as severe in matrix mechanics and completely absent in the path integral formulation. wikipedia - Schrodinger equation
Born Oppenheimer approximation
equation of forces
Figure 14.12 - Triple Equations to Represent a Single Sympathetic Event
On the Partial Differential Equations of Mathematical Physics
Eighteen Attributes or Dimensions
3.23 - Hydrodynamic Equations - Vortex Motions
9.30 - Eighteen Attributes of a Wave
12.11 - Eighteen Attributes or Dimensions
14.36 - Triple Equations