matrizelement

Matrizelement is a term used in quantum mechanics and quantum field theory. It refers to a specific number that characterizes the probability amplitude of a transition between two quantum states. When describing a physical process, such as the interaction of a particle with a force field or the decay of an unstable particle, the system evolves from an initial state to a final state. The matrizelement quantifies how likely this transition is to occur.

Mathematically, a matrizelement is typically represented as a scalar value obtained by taking the inner product of the final state with an operator acting on the initial state, or vice versa, depending on the convention used. The operator in question represents the interaction or perturbation that causes the transition. For example, in quantum electrodynamics, the matrizelement for an electron scattering off a photon involves the electromagnetic interaction operator.

The calculation of matrizelements is a fundamental task in theoretical physics. It often involves complex integrals and sums over various degrees of freedom. The square of the magnitude of a matrizelement is directly proportional to the probability of the corresponding transition occurring. Therefore, by computing matrizelements, physicists can predict the outcomes of experiments and understand the dynamics of quantum systems. Different physical phenomena will have different operators associated with them, leading to distinct matrizelements and, consequently, different observable probabilities.