Matrizelements

Matrizelements is a term used in quantum mechanics and quantum field theory. It refers to the components of a matrix that represent operators acting on a quantum system. Specifically, if there is an operator A and a set of basis states |i⟩ and |j⟩, the matrizelement of A between these states is given by the bra-ket notation ⟨i|A|j⟩. This value is a complex number that quantifies the strength of the transition from state |j⟩ to state |i⟩ induced by the operator A.

These matrizelements are fundamental for calculating observable quantities. For instance, in spectroscopy, the probability of an atom absorbing or emitting a photon of a specific energy is proportional to the square of the matrizelement of the interaction Hamiltonian between the initial and final atomic states. Similarly, in quantum field theory, matrizelements of scattering operators are used to determine the probabilities of various particle interactions. The choice of basis states significantly influences the form of the matrix but not the physical predictions derived from these matrizelements. Calculating these values often involves integrating over the wavefunctions of the states involved and the operator itself.