Search results
After the failure of the Bohr atomic model to comply with the Heisenberg’s uncertainty principle and dual character proposed by Louis de Broglie in 1924, an Austrian physicist Erwin Schrodinger developed his legendary equation by making the use of wave-particle duality and classical wave equation.
Wave mechanics and the Schr¨odinger equation Although this lecture course will assume a familiarity with the basic concepts of wave mechanics, to introduce more advanced topics in quantum theory, it makes sense to begin with a concise review of the foundations of the subject.
In most cases, one can start from basic physical principles and from these derive partial differential equations (PDEs) that govern the waves. In Section 4.2 we will do this for transverse waves on a tight string, and for Maxwell’s equations describing electromagnetic waves.
We derive the wave equation from F = ma for a little bit of string or sheet. The equation corresponds exactly to the Schrödinger equation for a free particle with the given boundary conditions. The most important section here is the one on waves on a sphere. We find the first few standing wave solutions.
intermediary of wave functions it would seem natural to also have at hand a corresponding wave equation to determine how the wave functions evolve through time and space. The Schrödinger wave equation, which serves this purpose, is not something that can be rigorously derived from first principles. Like many other instances in physics,
These are the lecture notes of a course on geometric wave equations which I taught at the University of Potsdam in the winter term 2015/2016. The course gave an introduction to linear hyperbolic PDEs on Lorentzian manifolds. The geometric setup allows to apply the theory in general relativity, for instance.
Visit the AMS home page at URL: http://www.ams.org/ Chapter 1. The Wave Equation. 1.1. Basic Notations and Concepts from Geometry. 1.2. Semilinear Problems. 1.3. Wave Maps. Chapter 2. 2.1. Variational Formulation. 2.2. Noether’s Theorem.
