Some Remarks Concerning Schrödinger's Wave Equation

Geo. D. Birkhoff

Viktor Trkal

P. Enders

This chapter introduces the paradigm ‘quantization as selection problem’ by means of few historical remarks. They include Einstein’s 1907 reasoning, Schrödinger’s 1926 derivation of his wave equation, and Gödel’s theorem and Munchhausen’s trilemma. The latter ones concern questions, which can be posed, but not be answered within CM. Such questions transcendent CM. This book poses the question, how the mechanics of oscillators without turning points looks like. (“oscillators without turning points” means oscillators, which may assume configurations beyond the classical turning points.)

John C. Morrison

John Morrison

Aaron C.H. Davey

The father of quantum mechanics, Erwin Schrodinger, was one of the most important figures in the development of quantum theory. He is perhaps best known for his contribution of the wave equation, which would later result in his winning of the Nobel Prize for Physics in 1933. The Schrodinger wave equation describes the quantum mechanical behaviour of particles and explores how the Schrodinger wave functions of a system change over time. This project is concerned about exploring the one-dimensional case of the Schrodinger wave equation in a harmonic oscillator system. We will give the solutions, called eigenfunctions, of the equation that satisfy certain conditions. Furthermore, we will show that this happens only for particular values called eigenvalues.