What is Central potential: Definition and 29 Discussions

In classical mechanics, a central force on an object is a force that is directed towards or away from a point called center of force.

F

=

F

(

r

)
=

|

F
(

r

)

|

r

^

{\displaystyle {\vec {F}}=\mathbf {F} (\mathbf {r} )=\left\vert F(\mathbf {r} )\right\vert {\hat {\mathbf {r} }}}
where

F

{\displaystyle \scriptstyle {\vec {\text{ F }}}}
is the force, F is a vector valued force function, F is a scalar valued force function, r is the position vector, ||r|| is its length, and

r

^

{\displaystyle \scriptstyle {\hat {\mathbf {r} }}}
= r/||r|| is the corresponding unit vector.
Not all central force fields are conservative or spherically symmetric. However, a central force is conservative if and only if it is spherically symmetric or rotationally invariant.

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1. I Separable Hamiltonian for central potential

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4. D

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5. D

Constants of motion in quantum mechanics

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7. I Free particle in a central potential

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16. Computing Central Force Potential: Bound from |r| to Infinity

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