The notation is deceptively simple. The elegant nature of the Dirac Bra-ket notation allows physicists to treat linear functionals represented as bras in a very intuitive fashion (they preserve nearly all of the familiar algebraic properties of numbers except commutativity). Computations of inner products are naturally suggested, and the problem is not bogged down in excessive notation -- it is essentially distilled down to its algebraic content alone.
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The notation is deceptively simple. The elegant nature of the Dirac Bra-ket notation allows physicists to treat linear functionals represented as bras in a very intuitive fashion (they preserve nearly all of the familiar algebraic properties of numbers except commutativity). Computations of inner products are naturally suggested, and the problem is not bogged down in excessive notation—it is essentially distilled down to its algebraic content alone.