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.

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