Understanding Parity in Quantum Mechanics

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Parity in quantum mechanics refers to the symmetry of a wave function under spatial inversion, specifically whether it is even or odd. An even function remains unchanged when the spatial coordinate is inverted, while an odd function changes sign. This concept is crucial in determining the behavior of quantum states and their interactions. Parity is relevant when the wave function is centered around the origin, impacting the physical properties of particles. Understanding parity helps clarify the fundamental symmetries in quantum systems.
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As part of an exam paper I've been using to revise with, I came across a question that simply says "What is parity?"

Well I know vaguely what it is. Its to do with whether a wave is odd or even right?

For example for cos and sin
odd parity occurs because sin(-x) = -sin(x)
and cos(-x) = cos(x) means that the function has even parity.

But I what I don't know is how I would word the answer to the question "What is parity?". How would you do it?

It only occurs (in the quantum-mechanical sense (very basic intro level)) if the wave function is centralised about the origin of the scale, right?

Any hints as how to go about answering this would be appreciated.
 
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