Canonical Hamiltonian density of a real scalar field
= Canonical Hamiltonian density of a real scalar field
{title2=$\mathcal H=\tfrac12\pi^2+\tfrac12|\nabla\phi|^2+V(\phi)$}
For a <real scalar field> with <Lagrangian density> $\mathcal L=\dot\phi^2/2-|\nabla\phi|^2/2-V(\phi)$, the <canonical momentum> is $\pi=\dot\phi$. Its <Hamiltonian density> is the sum of momentum energy, gradient energy and potential energy. Hamilton's equations recover the <Euler-Lagrange equation>.