Probability amplitude

It is a complex number.

For example, as we seen earlier in Superposition

∣ψ⟩=ψ0∣ψ0⟩+ψ1∣ψ1⟩\ket{\psi}=\psi_0\ket{\psi_0}+\psi_1\ket{\psi_1}

In this case, ψ0\psi_0 and ψ1\psi_1 are probability amplitudes.

Note that the sum of all probability amplitudes squared add up to one.

∑n∣ψn∣2=1\sum_n |\psi_n|^2 = 1

Another example is in Born Rule

Pψn=∣⟨ψn∣ψ⟩∣2\begin{gather*} P_{\psi_n}=|\left\langle \psi_n|\psi \right\rangle|^2 \end{gather*}

In this case, ⟨ψn∣ψ⟩\braket{\psi_n|\psi} is the probability amplitude. You could write it

ψn=⟨ψn∣ψ⟩\psi_n=\braket{\psi_n|\psi}

BE CAREFUL ∣ψn⟩\ket{\psi_n} is an STATE VECTOR, ψn\psi_n is a probability amplitude which is a COMPLEX NUMBER. Notation is really confusing in QM.