👉 In mathematics, a commutator is a mathematical operation that takes two elements and returns the product of those elements. In other words, it's like taking the reciprocal of the multiplication of two numbers. For example: - \(a \times b\) (which stands for "a times b") is the same as \(b \times a\). So, if we have two elements \(a\) and \(b\), then their commutator is \(ab\). It's like saying
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What is the definition of Commutators? 🙋
👉 The commutator of two operators $A$ and $B$, denoted by $[A,B]$, is defined as: $$ [A,B] = AB - BA $$ This operation is important in quantum mechanics because it allows us to manipulate the phase of a state, which can be crucial for understanding the behavior of quantum systems.
