Quantum Mechanics (1) · Problem 4.7

The density matrix formulation

Physics — Quantum Mechanics · density-matrix-hermitian-operators-hilbert-space

Problem

Consider an

N

-dimensional Hilbert space. We define the real vector space,

\mathcal{O}

of Hermitian operators on this Hilbert space. We define a scalar product on this vector space according to:

(x, y) = \mathrm{Tr}(xy), \quad \forall x, y \in \mathcal{O}.