I had missed this question.

Most potentials physicists use to model the behavior of atoms and molecules, are symmetric in space. When the potential is unknown it is usual to guess at a first term in a Taylor expansion . For symmetric potentials the first term in a Taylor series expansion is the x**2, and that is why the use of the harmonic oscillator is ubiquitous.

The current prominent theory of everything for particle physics is string theory , where particles are vibrational modes on the basic two dimensional string. It is amusing to think that maybe this also is a first approximation to a much more complicated formalism.

I had missed this question.

Most potentials physicists use to model the behavior of atoms and molecules, are symmetric in space. When the potential is unknown it is usual to guess at a first term in a Taylor expansion . For symmetric potentials the first term in a Taylor series expansion is the x**2, and that is why the use of the harmonic oscillator is ubiquitous.

The current prominent theory of everything for particle physics is string theory , where particles are vibrational modes on the basic one dimensional string. It is amusing to think that maybe this also is a first approximation to a much more complicated formalism.