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 ${\displaystyle J}$

${\displaystyle J=\oint {p_{j}\mathrm {d} q_{j}}}$,

where a generalized position coordinate and the associated generalized impulse are and are integrated over a period. ${\displaystyle q_{j}}$ ${\displaystyle p_{j}}$

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 .