Hcdot
Hcdot, usually written as H⋅, is a notation used primarily in theoretical physics and applied mathematics to denote a specific type of inner product that involves a Hamiltonian operator. The symbol Hcdot represents the action of the Hamiltonian H on a state vector or function, followed by a dot or scalar product with another vector or function, resulting in a scalar quantity that often corresponds to an observable or energy expectation value. The notation is concise and distinguishes itself from other forms of the dot product that involve unrelated vectors or operators.
In quantum mechanics, Hcdot plays a pivotal role in the time‑evolution equation for wavefunctions. For a wavefunction
Beyond quantum theory, Hcdot occasionally appears in the study of lattice models in statistical mechanics, where
Although the notation is not universally standard—some authors replace Hcdot with Hψ or 𝐻ψ to signify the