To represent the state of a quantum particle, or a quantum system, we introduce the “ket vector”. This is just an abstract mathematical notation, a compact way of saying “the state of this particle”. ...To represent the state of a quantum particle, or a quantum system, we introduce the “ket vector”. This is just an abstract mathematical notation, a compact way of saying “the state of this particle”. The name “ket” is the latter half of the word “braket”, a misspelling of bracket.