Before the 20th century, light was thought to be a wave, and classical wave theory could describe its properties and its behaviour. However, the works of various physicists, most notably Max Planck, Albert Einstein and Erwin Schrödinger, found light to possess particle-like properties also. The idea that light could possess both wave-like and particle-like properties, named wave-particle duality, did not agree with classical physics. A new set of theories were required to explain such unusual behaviour, and thus came the birth of quantum mechanics in the early 20th century.

The behaviour of objects we see in everyday life generally follow classical physics, and this is because such objects have a very large mass. Quantum effects are negligible at this scale of physics. However, as we delve into the world of photons, electrons and other particles with extremely low mass, quantum mechanics plays a significant role in describing their properties and their behaviour. In this post I will aim to explain some of the basic theories that underpin quantum mechanics.

**The Wavefunction**

A quantum mechanical system can have multiple states. The ground state has the least energy, the first excited state has higher energy, and the second excited state has even higher energy, and so on. Each state is associated with a wavefunction (denoted by the Greek letter psi, Ψ), which describes everything there is to know about the state. Wavefunctions are important because on this scale of physics, even particles exhibit wave-like nature.

The wavefunction has a special property that its square gives the probability distribution of the particle existing at a particular position. This is one of the key features of quantum mechanics – we cannot pinpoint exactly where a particle is, but instead we can only calculate the probability that a particle exists at a location.

**Quantisation of Energy**

Another key feature of quantum mechanics is that energy is discrete, i.e. it must take on specific values. The term ‘quantum’ refers to a ‘packet’ of a physical quantity (e.g. energy), hence the name quantum mechanics. This is a reason why a quantum system has discrete states, each of which is also associated with a specific amount of energy.

**Heisenberg’s Uncertainty Principle**

Okay, so if we made measurements of a particle, surely we don’t need to use the wavefunction anymore? The issue with particles this small is that we can never know its properties exactly, no matter how good our measuring instruments are. This is a consequence of Heisenberg’s uncertainty principle:

The equation shows that the more precisely we know about the position of a particle, the less we know about its momentum, and vice versa. ħ/2 has an extremely small value of about 5.27×10^{-35} Js, so thus this principle has a negligible impact on a human scale.

What if we don’t try and measure the position of a particle directly, and instead confine it within a certain area so that it can’t escape? Another issue arises as a result of the uncertainty principle – confinement energy. You can prove from the principle that as you confine a particle to smaller area, the energy needed to confine it rises. If you want to confine the particle enough so that the uncertainty in its position is zero, the energy required is infinite… so yeah.

These are a few of the many intriguing aspects of quantum mechanics. Quantum mechanics may seem very counter-intuitive but it is supported by solid mathematical calculations and it agrees with experimental data, which is what a good theory should do.

*Yanhao*

Even though I don’t understand all the symbols and abbreviations, this article gives me a little window of insight into a subject that has always fascinated me. Thank you.

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