A Casual Guide to Dirac Notation

A Casual Guide to Dirac Notation

The notion of quantum mechanics has been around for almost one hundred years. In spite of this, it remains a very difficult subject to learn and comprehend due to competing theories and probabilistic nature(as illustrated by Bohr’s quote).

Quantum Mechanics

“If you are not completely confused by quantum mechanics, you do not understand it.” — Niels Bohr

The notion of quantum mechanics has been around for almost one hundred years. In spite of this, it remains a very difficult subject to learn and comprehend due to competing theories and probabilistic nature(as illustrated by Bohr’s quote). However difficult to grasp, there still remain profound theories that are the backbone of modern quantum mechanics. One of the more interesting applications of quantum mechanics, specifically for my own research, is in the realm of quantum computing. This is by no means an article explaining superposition, entanglement, or the potential for parallel worlds. Nevertheless, I want to introduce common notation used when discussing these topics — when you read about them, you will have a general understanding of the systems they are describing.

Kets

Let’s take a look at a traditional vector in a 3-dimensional space…

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Basis vectors in 3-dimensional space are defined as…

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More generally, basis vectors, regardless of dimensionality, are denoted as…

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This means any vector can be decomposed into a linear combination of basis vectors…

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Similarly using Dirac notation, a ket can be used to denote a vector…

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Basis vectors can also be written as kets…

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This means we can decompose our original vector into a linear combination of basis vectors using kets…

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science quantum-mechanics physics quantum-physics mathematics data science

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