Wave Functions
Soon after de Broglie introduced his hypothesis
to the world, a period which is often referred to as the old quantum mechanics
came to an end (1900 – 1925). The basic phenomena of the old quantum mechanics
are the quantization of energy and the wave-particle duality. Since 1925 we are
dealing with the modern quantum mechanics.
Austrian physicist Erwin Schrödinger in 1925
adjusts de Broglie’s inaccurate theory and assigns a so-called wave function to
every quantum object. Temporal and spatial evolution of a wave function is
described by a complex equation, the so-called Schrödinger equation. A wave
function is denoted by the capital or lowercase Greek letter psi:
𝜳, 𝝍
The
wave function is a complex mathematical function in which all the properties of
a given quantum objects (momentum, position, etc.) are stored (this is
different from the de Broglie’s matter wave, since de Broglie did not assign
this property to his wave, moreover, he perceived the wave as a physical
object, while Schrödinger’s wave function is merely abstract). This set of
properties of a quantum object is called a quantum state. Quantum state is
denoted as follows:
|𝝍⟩
The wave function is presumably the most significant idea of quantum mechanics, since most of the phenomena of the modern quantum mechanics are derived from it. Some of these phenomena, especially the principle of quantum superposition, are so different from the ones which are usual for us in the macroworld that it is often very difficult to believe, let alone understand them.