Of course the kinetic energy is , with . The sum of kinetic and potential energy can be written in the form
(2.3) |
Actually, this form is not very convenient for quantum mechanics. We rather work with the so-called momentum variable . Then the energy functional takes the form
(2.4) |
The energy expressed in terms of and is often called the (classical) Hamiltonian, and will be shown to have a clear quantum analog.