Introductory Quantum Mechanics II: The Schrödinger Equation

Yang Fujia, J. H. Hamilton

Theory of Relativity The Configuration of Atoms: Rutherford's Model Quantum States of Atoms: The Bohr Model Fine Structure in Atomic Spectra: Electron Spin Atoms Containing Many Electrons: The Pauli Exclusion Principle X-Rays Introductory Quantum Mechanics I: Concepts Introductory Quantum Mechanics II: The Schrodinger Equation Basic Concepts of Nuclear Physics Radioactive Decay Nuclear Forces and Nuclear Models Nuclear Interaction and Reactions Hyperfine Interactions High-Energy Physics

Nielsen, M. P., Laugesen, Jacob, Sanjayan, J. G.

Stanley M. Flatté

The use of the Schrödinger equation in classical physics was begun in 1950; in the classical context it is known as the parabolic wave equation. The derivation of the parabolic wave equation from the full classical wave equation is analogous to deriving the Schrödinger equation from the Klein–Gordon equation. An introduction to the Schrödinger equation by this route could be of help in introductory quantum-mechanics classes.

акустика Механика

Jorge Pinochet

Abstract A heuristic derivation of the one-dimensional Schrödinger equation is presented based on an energy interpretation of the wave function. The spatial derivative naturally produces a term proportional to the kinetic energy, while the temporal derivative yields a term proportional to the total energy. By relating both contributions through the classical relation for total mechanical energy, the Schrödinger equation is obtained. The proposed approach provides a simple and intuitive framework to introduce this equation in modern physics or introductory-level quantum mechanics courses.