Here's a video that describes the history of quantum and electron orbitals and configurations a little bit: Crash Course Chemistry: The Electron
Here's a video that describes some of these concepts: The Wave Behavior of Matter, by DCaulf, on YouTube
The "New Quantum Mechanics" was introduced a little after the "Old Quantum Mechanics" which was developed by Planck and Bohr. This is when quantum mechanics became very confusing to people. In the old quantum theory, we could think about particles moving in normal ways. The electrons orbit the nucleus just like planets orbit the sun. But this was wrong. The new quantum theory says that tiny particles behave in ways that are totally different from normal objects that we can see, like basketballs or planets. In fact, it is impossible to know exactly where they are or what they do.
Einstein had convinced physicists that light was a particle (now
called photon) in 1905. Later, in 1925, de Broglie proposed that
particles like electrons could also be waves. De Broglie was a
French prince who was initially interested in history, but during
World War I he joined the army as a radio operator and became
interested in waves. He was also a lover of music. These qualities
lead him to interpret Bohr's atoms as "musical instruments". Bohr
assumed that his energy levels were quantized, but didn't explain
why. De Broglie proposed that quantization arose from
the same effects as the quantized frequencies (fundamental and
overtone) present in a guitar string, that make it work as an instrument. (Review standing waves in this section if needed.) De Broglie thought that
electrons in "orbits" like in the Bohr model were like strings on
instruments. A string has to have nodes at each end; an electron in
an orbit also has to be a standing wave, with a whole number of
wavelengths around its path. In other words,
nλ = 2π r
where n is an integer. Thus, the wave interferes constructively with
itself when it makes a full circle.
| λ = | h |
| mv |
Heisenberg developed a way to work with the allowed energies of atoms using matrices. He believed that we must work with the quantities we can observe experimentally, like energies (via spectroscopy). This led him to the Uncertainty Principle which says that certain pairs of quantities (position and momentum, energy and time) can't be measured precisely at the same time. For instance, if you want to know exactly where a particle is, you can't also know exactly what its velocity is. This was part of the new "statistical" quantum mechanics. In classical mechanics, you can know everything about particles (like balls): exactly where they are, exactly where they are going, and predict exactly the results of collisions or other events. In the new quantum mechanics, it was argued that this perfect knowledge of particles was simply impossible. For instance, exactly where is a wave?
Although Heisenberg's matrix quantum mechanics is probably used more often because it works well with computer calculations, an equivalent description developed by Schrodinger gives more intuition, so we will describe it in detail. The methods give the same answers but use very different math. Schrodinger extended de Broglie's theory by applying well-known physics of waves (for instance, in instruments) to describe electrons. There's a detailed example in the next section.