# 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

Richard Montgomery, University of California, Santa Cruz

**Friday, October 20, 2017**

**Gabriel Martins****Friday, October 27, 2017**

No Seminar

No Seminar

**Friday, November 3, 2017**

No Seminar

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

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.

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 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

Holiday - No Seminar

**Friday, December 1, 2017**

**Connor Jackman, University of California, Santa Cruz**

*The Hydrogen Atom***Friday, December 8, 2017**

No Seminar

No Seminar

**Friday, December 15, 2017**

No Seminar

No Seminar