Of course the kinetic energy is {1\over 2}m{v}^{2}, with v =\dot{ r} = {d\over dt}r. The sum of kinetic and potential energy can be written in the form
|
E = {1\over
2}m{v}^{2} + V (r).
| (2.3) |
Actually, this form is not very convenient for quantum mechanics. We rather work with the so-called momentum variable p = mv. Then the energy functional takes the form
|
E = {1\over
2} {{p}^{2}\over
m} + V (r).
| (2.4) |
The energy expressed in terms of p and r is often called the (classical) Hamiltonian, and will be shown to have a clear quantum analog.