State space, kets and brackets কী?

The states of a quantum system form a complex vector space with an inner product — a Hilbert space $\mathcal H$ (the mathematics is developed in the Year 3 mathematics volume). A state is a vector, written as a ket $\ket\psi$, normalised: $\braket\psi\psi = 1$. The inner product of two states is the complex number $\braket\varphi\psi$, conjugate-linear in the first slot, with $\braket\varphi\psi = \braket\psi\varphi^*$. In an orthonormal basis $\{\ket{e_i}\}$,

The wave function of the previous chapters is the family of components of $\ket\psi$ along position: $\psi(x) = \braket{x}{\psi}$; nothing is lost, and systems with finite state spaces — undreamable as waves — become describable.