What is Bra-ket Notation?

Bra-ket notation is concise and useful.

A wavefunction is represented by a ket ( \psi\rangle).
The complex conjugate of wave function is written as a bra (\langle\psi ).

The complex conjugate of a variable is found by swapping the sign of the imaginary part of said variable’s complex number, in other words: reflecting z across the real axis. For example, \(z = x + iy\) \(z^* = x - iy\)

A bra on the left and a ket on the right implies integration over dt. \(\langle\psi \psi\rangle \equiv \int\psi^*\psi dt\)
Similarly \(\langle\psi \hat{X} \psi\rangle \equiv \int\psi^*\hat{X}\psi dt\)

My brief tutorial covered the basic usages of bra-ket notation in a quantum mechanical context; bra-ket notation is also used elsewhere.

Written on December 11, 2013