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2.2 Energy function

Of course the kinetic energy is $ {\frac{1}{2}}$mv2, with v = $ \dot{\vec{r}}$ = $ {\frac{d}{dt}}$r. The sum of kinetic and potential energy can be written in the form

E = $ {\frac{1}{2}}$mv2 + 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 = $ {\frac{1}{2}}$$\displaystyle {\frac{\vec{p}^{2}}{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.

© 1998 Niels Walet, UMIST
Email Niels.Walet@umist.ac.uk