Tilladte energiniveauer: Schrödingerligningen og Rydbergs formel

This study examines how to describe the allowed energies for particles in different situations. In the first place this study describes the allowed energies for a particle in a finite square well and subsequently the allowed energies for the electron in a hydrogen atom which will be used to prove the Rydberg formula. Afterwards this study will demonstrate the Rydberg formula experimentally, too. In the problem about the particle in a square well in a finite square well, also the time independent wave function for the particle, ?(x), will be described. In this connection this study will account for why normalization can be used to determinate the wave function. This study also argues for the fact that the Schrödinger equation can be written independent of the time and therefore the only variable is the placement of the particle. The Schrödinger equation also contents complex numbers which this study describes, too. The Schrödinger equation is built up as a differential equation of second order which this study examines, too, what this fact represents.

Indhold

Indledning3

Schrödingerligningen4

2. ordens differentialligninger4

Komplekse tal8

Kompleks konjugering11

Tidsuafhængighed12

Normalisering14

Den endelige brønd20

Lige- og ulige funktioner23

Bølgefunktionen26

Energiniveauerne for en partikel i en endelig brønd30