Effective Potential - Important Properties

Important Properties

There are many useful features of the effective potential. The condition for a particle of energy E flying by to be `trapped' and go into an orbit:

To find the radius of a circular orbit, we simply minimize the effective potential with respect to, or equivalently set the net force to zero and then solve for :

After solving for, plug this back into to find the maximum value of the effective potential

To find the frequency of small oscillations:

where the double prime indicates the second derivative of the effective potential with respect to .

Read more about this topic:  Effective Potential

Famous quotes containing the words important and/or properties:

    Childhood is an adventure both for children and for their parents. There should be freedom to explore and joy in discovery. The important discoveries for both parents and children seldom come at the points where the path is smooth and straight. It is the curves in that path to adventure that make the trip interesting and worthwhile.
    Lawrence Kutner (20th century)

    A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.
    Ralph Waldo Emerson (1803–1882)