**Introduction**

Massive atomic nuclei are born naked, but their net positive charge, Z, quickly attracts Z comparatively mass-less electrons to produce neutral atoms.

- The nucleus of a neon atom – atomic number 10 and so the Ne
^{10+}ion – attracts 10 negatively charged electrons to give an atom of neon.

The negatively charged electrons do not *nuclear react* with the positively charged protons of the nucleus, as they do inside neutron stars, instead they associate as three dimensional resonant standing waves.

*The electrons move about the point positive chargein a beautiful and subtle quantum mechanical dance*

- The modes of resonance for single electron systems such as the hydrogen atom are described by the Schrödinger wave equation.
- Schrödinger knew of de Broglie's proposal that a moving particle has wavelength,
*l*, proportional to Plank's constant,*h*, and momentum*p*so that*l = h/p,*a property we now known as wave-particle duality. - Schrödinger constructed a differential equation for a wavelike electron resonating in three dimensions about a point positive charge (Wikipedia):
- Solutions to the Schrödinger wave equation correspond to modes of electron resonance and are formally called wavefunctions.
- Wavefunctions assume discrete, or quantised, energies and have energies which correspond to the spectral lines of one electron atoms and ions of the type: H
^{•}, He^{+}, Li^{2+}, Be^{3+}, etc. - Although not exactly the same, chemists tend to call wavefunctions "orbitals".

**1-Dimensional resonant standing waves**, the vibrating string:

**2-Dimensional resonant standing wave**, a vibrating drum skin (see QuickTime movies here andhere):

**3-Dimensional resonant standing waves**, atom wavefunctions from the Schrödinger wave equation:

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