TIME-DEPENDENT EQUATION (GENERAL)
This is Erwin Schrodinger’s Time-Dependent Equation (general). This gives a description of a system evolving with time.
TIME-DEPENDENT NON-RELATIVISTIC SCHRODINGER EQUATION
- The most famous example is the non-relativistic Schrödinger equation for a single particle moving in an electric field. Where M is the particle’s mass, V is the potential energy, ∇2 is the Laplacian, and Ψ is the wave function. But if you didn’t get all that, in human language this means the total energy equals the potential energy plus the kinetic energy. This is a Partial Differential Equation. A Partial Differential Equation is a differential equation (an unknown function of one, or several variables) that contains unknown multivariable functions (an extension of calculus with more than one variable used) and their partial derivatives (part of a derivative. Derivative is a measure of how a function changes as its input changes).
TIME-INDEPENDENT GENERAL SCHRODINGER EQUATION
This is the general, Time-Independent Schrodinger Equation. This equation predicted that wave functions can form standing waves, also known as “orbitals”.
TIME-INDEPENDENT NON-RELATIVISTIC SCHRODINGER EQUATION
This is the non-relativistic Time-Independent Schrodinger Equation. This equation does the same thing as the general, although, it is for a situation with a single particle moving in an electric field.