Effective potential

The effective potential (also known as effective potential energy) is a mathematical expression combining multiple (perhaps opposing) effects into a single potential. In classical mechanics it is defined as the sum of the 'opposing' centrifugal potential energy with the potential energy of a dynamical system. It is commonly used in calculating the orbits of planets (both Newtonian and relativistic) and in semi-classical atomic calculations, and often allows problems to be reduced to fewer dimensions.

The effective potential ${\displaystyle U_{\text{eff}}}$ is defined in the following way:

${\displaystyle U_{\text{eff}}(\mathbf {r} )={\frac {L^{2}}{2\mu r^{2}}}+U(\mathbf {r} )}$

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