Premium
Kinetic Energy Partition Method for Competing Modes
Author(s) -
Mineo Hirobumi,
Chao Sheng D.
Publication year - 2014
Publication title -
journal of the chinese chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 45
eISSN - 2192-6549
pISSN - 0009-4536
DOI - 10.1002/jccs.201400008
Subject(s) - kinetic energy , chemistry , eigenfunction , hamiltonian (control theory) , partition (number theory) , potential energy , eigenvalues and eigenvectors , harmonic oscillator , quantum mechanics , statistical physics , classical mechanics , physics , mathematics , mathematical optimization , combinatorics
We present a new basis set expansion method for quantum dynamics systems with two competing modes where the interaction potentials are equally dominant. The new idea introduced here is a kinetic energy partition scheme instead of the usual division of the potential energy. The partition results in two kinetic energy terms with their effective masses. By distributing each partial kinetic energy to the respective potential, the full Hamiltonian can be expressed as the sum of the two competing modes. The solution procedure is illustrated by using a system consisting of a particle under the action of two harmonic potentials with different equilibrium distances and force constants. Next we apply this method to obtain the potential energy curves for the prototype hydrogen molecule ion. This new expansion converges very fast to the exact solutions for both eigenvalues and eigenfunctions.