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SUMMARY:Two Hundred Years after Hamilton: Exploring New Formulations of Cl
 assical and Quantum Mechanics
DTSTART:20251113T151500
DTEND:20251113T161500
DTSTAMP:20261005T200137Z
UID:2833d6e85dedca0e89ed12df75ea7c48751017fd3408aacf461bfcca
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. David J. Tannor\nDepartment of Chemical and Biological P
 hysics\nWeizmann Institute of Science\nThis talk has three parts. The firs
 t part is an introduction to Hamilton's two monumental papers from 1834-18
 35\, which introduced the Hamilton-Jacobi equation\, Hamilton’s equation
 s of motion and the principle of least action [1]. These three formulation
 s of classical mechanics became the three forerunners of quantum mechanics
 \; but ironically none of them is what Hamilton was looking for - he was l
 ooking for a "magical" function\, the principal function S(q1\, q2 \, t) f
 rom which the entire trajectory history can be obtained just by differenti
 ation (no integration) [2]. In the second part of the talk I argue that Ha
 milton’s principal function is almost certainly more magical than even H
 amilton realized. Astonishingly\, all of the above formulations of classic
 al mechanics can be derived just from assuming that S(q1\, q2\, t) is addi
 tive\, with no input of physics [3]. The third part of the talk will prese
 nt a new formulation of quantum mechanics in which the Hamilton-Jacobi equ
 ation is extended to complex-valued trajectories [4]\, allowing the treatm
 ent of classically allowed processes\, classically forbidden process and a
 rbitrary time-dependent external fields within a single\, coherent framewo
 rk. The approach is illustrated for barrier tunneling\, wavepacket revival
 s\, nonadiabatic\ndynamics\, optical excitation using shaped laser pulses 
 and high harmonic generation with strong field attosecond pulses [5].\n\n1
 . W. R. Hamilton\, On a General Method in Dynamics\, Philosophical Transac
 tions\, Part 2\, p. 247 (1834)\; ibid.\, Second Essay on a General Method 
 in Dynamics\, Part 1\, p. 95 (1835).\n2. M. Nakane and C. G. Fraser\, The 
 Early History of Hamilton-Jacobi Dynamics 1834-1837\, Centaurus 44\, 161 (
 2002)\; C. Lanczos\, The Variational Principles of Mechanics (Oxford\, 194
 9)\n3. D. J. Tannor\, New derivation of Hamilton’s three formulations of
  classical mechanics (preprint)\; ibid\, Duality of the Principle of Least
  Action: A New Formulation of Classical Mechanics\, arXiv:2109.09094 (2021
 ).\n4. Y. Goldfarb\, I. Degani and D. J. Tannor\, Bohmian mechanics with c
 omplex action: A new trajectory based formulation of quantum mechanics\, J
 . Chem. Phys. 125\, 231103 (2006)\; J. Schiff\, Y. Goldfarb and D. J. Tann
 or\, Path integral derivations of complex trajectory methods\, Phys. Rev. 
 A 83\, 012104 (2011)\; N.Zamstein and D. J. Tannor\, Overcoming the root s
 earch problem in complex quantum trajectory calculations\, J. Chem. Phys. 
 140\, 041105(2014).\n5. N. Zamstein and D. J. Tannor\, Non-adiabatic molec
 ular dynamics with complex quantum trajectories. I. The adiabatic represen
 tation\, J. Chem. Phys. 137\, 22A518 (2012)\; W. Koch and D. J. Tannor\, W
 avepacket revivals via complex trajectory propagation\, Chem. Phys. Lett. 
 683\, 306 (2017)\; W. Koch and D. J. Tannor\, A three-step model of high h
 armonic generation using complex classical trajectories\, Annals of Physic
 s\, 427\, 168288 (2021).
LOCATION:CH G1 495 https://plan.epfl.ch/?room==CH%20G1%20495
STATUS:CONFIRMED
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