Quantum Harmonic Oscillator

Background to classical mechanics

Classical mechanics is a branch of physics that studies the motion of physical bodies. Sir Isaac Newton could come up with laws to explain the behavior of matter as far as motion is concerned. Later on, the particulate nature of matter was studied as a branch of physics. A particle of matter is the smallest divisible part of matter that interacts with the natural environment. The study of this infinitesimal particle is called quantum physics. The idea behind studying particles is that how it behaves will help us understand how the entire mass of matter behaves. Classical mechanics had conducted enough research on the harmonic oscillation of bodies such as a pendulum and a spring. Research by physicists on the quantum motion had established there exists motion of particles in a vibrational manner.

Quantum Harmonic Oscillator

Quantum harmonic oscillation defined

Quantum harmonic oscillation is the periodic vibration of atoms of a molecule about an equilibrium position. A scientist called Schrodinger come up with a mathematical equation explaining the energy of atoms and the wave nature of a particle. A Quantum harmonic oscillator is a model to demonstrate this harmonic oscillation, it uses bi-atomic molecular in a one-dimensional linear motion. The two diatomic molecules behave like two body masses attached to a linear spring on both ends and potential energy held by one body. The body with potential energy moves towards the equilibrium and farther transmits energy to the other body. The other body will thereafter transmit energy to the first body and this exchange of potential energy through to and fro movement creates a periodic vibration of the molecule. The frequency of vibration is fixed as a discreet amount of energy is transmitted therefore harmonic oscillations are produced.

Causes of harmonic oscillation

The oscillations exist owing to the energy possessed by these atoms. It is key to observe that the energy is absorbed from the ambient environment of the molecule. The higher the temperature (energy) the larger the vibration and the faster they become. Only at absolute zero degrees on the Kelvin scale does the atoms lack any energy to absorb and therefore do not vibrate. A zero degrees Celsius which is 273K the atoms have enough energy to vibrate, this is called zero scale vibration. Increases in the magnitude of vibration explain why matter expands when heated and contract when cooled. This is very key in material science.

The demonstration serves to explain that the behavior of matter is caused by the behavior of its minute particles i.e., the atoms and the subatomic particles, and how they interact with each other. The diatomic one-dimensional model is for demonstration only however molecules are multi-atomic and the vibration is multidirectional.  Science explains how everything works and this is done from the smallest indivisible particle. But is the knowledge of any help to man?

Importance of quantum harmonic oscillation

The importance of understanding nature cannot be overestimated. We interact on a day-to-day basis. We live on it and depend on it for survival. Take for example the air we breathe, there must be oxygen and therefore the constituents of air are important. The sun and man ignited fire or heat raises the temperature, the result is that matter expands. If we are ignorant of the expansion and contraction principle our bridges and rails could be collapsing even before completion. The harmonic oscillation of matter such as quartz has been used in the design of clocks and watches, medical and lab instruments, microprocessor-controlled devices and match more. Without science there cannot be technology and technology is the song of man in this 21st century.


The engineering field borrows heavily from physics. Provided there are physicists in the laboratory there will be engineers in worship designing that next big thing. Thanks to the quantum behavior of matter man have been able to produce light, sound, the motion of automobile, medical equipment, airspace navigation just to mention but a few. Hey you, quantum physics is no longer a hard nut to crack, you just need to crack small at a time. The small progress will make you an expert in no time. What is the next thing you want to learn?