Quantum Mechanics and Geometry Seminar Fall 2017
McHenry Library Room 1247
For further information please contact Professor Richard Montgomery or call 831-459-2400
Friday, September 29, 2017
Richard Montgomery, University of California, Santa Cruz
Friday, October 6, 2017
Richard Montgomery, University of California, Santa Cruz
Friday, October 13, 2017
Richard Montgomery, University of California, Santa Cruz
Friday, October 20, 2017
Gabriel Martins
Friday, October 27, 2017
No Seminar
Friday, November 3, 2017
No Seminar
Friday, November 10, 2017
No Seminar
ROOM CHANGE: McHenry 4130
Friday, November 17, 2017
Alexander Turbiner, Nuclear Science Institute, National Autonomous University of Mexico
Quantum n-body Problem: Generalized Euler Coordinates (from J-L Lagrange to Figure Eight and Ter-Martirosyan, then and today)
The potential of the $n$-body problem, both classical and quantum, depends only on the mutual, or relative, distances between bodies. By generalized Euler coordinates we mean relative distances and angles.
The NEW IDEA is to study trajectories (classical) and eigenstates (quantum) which depends on relative distances ALONE.
We show how this study is equivalent to the study of
(i) the motion of a particle ( quantum or classical) particle in curved space of dimension $n(n-1)/2$-dimensional
or the study of
(ii) the Euler-Arnold (quantum or classical) - $sl(n(n-1)/2)$ algebra top.
The curved space of (i) has a number of remarkable properties. In the 3-body case the {\it de-quantization} of quantum Hamiltonian leads to a classical Hamiltonian which solves a ~250-years old problem posed by Lagrange on 3-body planar motion.
Alexander Turbiner, Nuclear Science Institute, National Autonomous University of Mexico
Quantum n-body Problem: Generalized Euler Coordinates (from J-L Lagrange to Figure Eight and Ter-Martirosyan, then and today)
The potential of the $n$-body problem, both classical and quantum, depends only on the mutual, or relative, distances between bodies. By generalized Euler coordinates we mean relative distances and angles.
The NEW IDEA is to study trajectories (classical) and eigenstates (quantum) which depends on relative distances ALONE.
We show how this study is equivalent to the study of
(i) the motion of a particle ( quantum or classical) particle in curved space of dimension $n(n-1)/2$-dimensional
or the study of
(ii) the Euler-Arnold (quantum or classical) - $sl(n(n-1)/2)$ algebra top.
The curved space of (i) has a number of remarkable properties. In the 3-body case the {\it de-quantization} of quantum Hamiltonian leads to a classical Hamiltonian which solves a ~250-years old problem posed by Lagrange on 3-body planar motion.
Friday, November 24, 2017
Holiday - No Seminar
Friday, December 1, 2017
Connor Jackman, University of California, Santa Cruz
The Hydrogen Atom
Friday, December 8, 2017
No Seminar
Friday, December 15, 2017
No Seminar
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