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The Kepler Problem (Part 4) | Azimuth

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The Kepler problem is the study of a particle moving in an attractive inverse square force. In classical mechanics, this problem shows up when you study the motion of a planet around the Sun in the Solar System. In quantum mechanics, it shows up when you study the motion of an electron around a proton in a hydrogen atom. In Part 2 we saw that the classical Kepler problem has, besides energy and the three components of angular momentum, three more conserved quantities: the components of the eccentricity vector! This was discovered long ago, in 1710, by the physicist Jakob Hermann. But thanks to Noether, we now know that in classical mechanics, conserved quantities come from symmetries. In the Kepler problem, conservation of energy comes from time translation symmetry, while conservation of the angular momentum comes from rotation symmetry. Which symmetries give conservation of the eccentricity vector? As we shall see, these symmetries are rotations in 4-dimensional space. These include

The Kepler Problem (Part 4) | Azimuth Azimuth Home About The Kepler Problem (Part 4) The Kepler problem is the study of a particle moving in an attractive inverse square force. In classical mechanics, this problem shows up when you study the motion of a planet around the Sun in the Solar System. In quantum mechanics, it shows up when you study the motion of an electron around a proton in a hydrogen atom. In Part 2 we saw that the classical Kepler problem has, besides energy and the three components of angular momentum, three more conserved quantities: the components of the eccentricity vector!

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