What is a wavefunction?

Is it possible for an object to be at two different places or different states at the same time?

According to classical physics, this is an aberration.

But how does quantum physics approach the raised question?
 In the core of quantum physics lies a mysterious equation which is known as the wavefunction. The wavefunction conceptualizes the behaviour of elementary particles such as electrons and also challenges the notion of only one reality.

As many possibly know, the wavefunction has no physical meaning and it is only a mathematical representation. (The picture on the right gives a good approximative representation of a wavefunction for an electron, where the probability of finding an electron is greater at maximum amplitude.)

According to the principles of quantum physics, an electron can be found at two different places at once and this has been observed through the wavefunction of the electrons. This theory was best explained by Erwin Schrodinger(an Austrian Physicist who developed a lot of fundamental theories about quantum physics).

The explanation was coined the Schrodinger's Cat, which challenged the notion of one reality and explained the theory of superposition in quantum physics.
(Well, this is just an explanation, as for a cat having a big mass, it will have a wavelength too small to be measured and hence would not act as a quantum object.)

He first thought of a closed box in which was present a cat and a substance in radioactive decay. The decay had a probability of 50% chance of occurring and if this was the case, the cat would die, or else, the cat would be alive.

The superposition theory of quantum theory stated that unless a person opened the box, the cat was considered in a blur probability of being both dead and alive. 

This is what Schrodinger stipulated and events similar to these occur in the quantum realm. (like an electron being at two different places at once)

The wavefunction is best used to describe the behavior of quantum objects and used to calculate properties such as their positions( average position and momentum, its direction inter alia). For example, to calculate the probability distribution(where we are more likely to find an electron), we just have to input the wavefunction in the Schrodinger's equation.
(Important: I said that we can find only the probability distribution due to the Heisenberg Uncertainty Principle which states that the actual position and velocity of an electron cannot be determined exactly, even in theory)
Well, wavefunction(ψ) is not just a number, it is more of a complex mathematical equation which sometimes may rely on imaginative numbers such as i, which is the square root of -1.

To gather things up, physicists use wavefunctions to understand the nanoscale world(quantum world) and can possibly calculate and predict a system's future behavior, but only as a certain probability.

Wavefunctions are more complex than what we can deem, but I hope that this concise and brief explanation was informative enough to bestow some knowledge upon you.
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Also, click the following link for more thrilling blogs about science by Mayur Nunkoo.
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