Phase integral (Hamilton mechanics)
The phase integral in the Hamilton formalism is a quantity in systems with a periodic orbit . The integral has the dimension of an effect . It is defined as
- ,
where a generalized position coordinate and the associated generalized impulse are and are integrated over a period.
In approximate solutions of quantum mechanics such as Bohr-Sommerfeld's atomic model and in the WKB approximation for stationary systems, this quantity must be a multiple of Planck's quantum of action .
literature
- Ernst Schmutzer: Basics of Theoretical Physics . 3. Edition. tape 1 . Wiley-VCH, 2005, ISBN 978-3-527-40555-8 , pp. 446 .