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**Example text**

Coherent means that the same wave, complex exponential or sine wave, with a certain frequency, forms the wave function. The coherence length is the length of a region over which light is coherent. 4 TIME-INDEPENDENT SCHRÖDINGER EQUATION Erwin Schrödinger evaluated the theory of de Broglie and became convinced that matter waves, as many other waves, are functions in three dimensions and solutions of a differential equation. Due to the boundary conditions, there are eigenvalues. It would be reasonable if there was a correspondence between these eigenvalues and the Bohr quantum numbers.

That equation is referred to as the wave equation or the Schrödinger equation. To solve the wave equation (see Chapter 5), we use the solutions of the time-independent equation. With boundary conditions, we obtain the motion of the wave packet. 6). The particle may move around inside the walls, where V(x) = 0. The electrons of a piece of metal are freely mobile inside the metal, that is, the box. 6 One-dimensional box. Wave functions for n = 1 and n = 2 are given. Note the boundary conditions. 13 Quantum Theory the so-called π electrons in an aromatic molecule, where the molecule is the box.

Anyway, this free-electron model is a rather good model for π systems. The electrons are not really free, but bound to the molecule, since V = ∞ outside. 17. It is then enough with a very small energy, for example, in the form of heat, to excite the electrons to higher levels. For heavy particles, the quantization is thus without any importance since almost any energy is possible. Quantization is most important for small particles such as electrons. Summarizing, there are many solutions to a time-independent SE, but only those that satisfy the boundary conditions correspond to reality.