Schrödinger Equation

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 28. Chapters: Fractional Schrodinger equation, Logarithmic Schrodinger equation, Nonlinear Schrodinger equation, Relation between Schrodinger's equation and the path integral formulation of quantum mechanics, Schrodinger field, Solution of Schrodinger equation for a step potential, Theoretical and experimental justification for the Schrodinger equation. Excerpt: In quantum mechanics, the Schrodinger equation is a partial differential equation that describes how the quantum state of some physical system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrodinger. In classical mechanics, the equation of motion is Newton's second law, and equivalent formulations are the Euler-Lagrange equations and Hamilton's equations. In all these formulations, they are used to solve for the motion of a mechanical system, and mathematically predict what the system will do at any time beyond the initial settings and configuration of the system. In quantum mechanics, the analogue of Newton's law is Schrodinger's equation for a quantum system, usually atoms, molecules, and subatomic particles; free, bound, or localized. It is not a simple algebraic equation, but (in general) a linear partial differential equation. The differential equation describes the wavefunction of the system, also called the quantum state or state vector. In the standard interpretation of quantum mechanics, the wavefunction 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. Like Newton's Second law, the Schrodinger equation can be mathematically transformed into other formulations such as Werner Heisenberg's matrix mechanics, and...