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Quantum‐classical transition equation with complex trajectories
Author(s) -
Chou ChiaChun
Publication year - 2016
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.25218
Subject(s) - morse potential , wave packet , quantum potential , schrödinger equation , physics , quantum , wave function , harmonic oscillator , quantum mechanics , transition of state , planck constant , quantum harmonic oscillator , quantum dissipation , classical mechanics
A quantum‐classical transition equation in complex space is derived in the framework of the complex quantum Hamilton–Jacobi formalism. The transition equation is obtained by subtracting a complex‐valued quantum potential term from the complex‐extended time‐dependent Schrödinger equation (TDSE). It is shown that the nonlinear transition equation is equivalent to a linear scaled TDSE with a rescaled Planck's constant. Employing the quantum momentum function defined by the gradient of the complex action, we can analyze the quantum‐classical transition of physical systems using complex transition trajectories. Complex transition trajectories are presented for the free Gaussian wave packet, the harmonic oscillator, and the Morse potential. This study demonstrates that the transition equation provides a continuous description for the quantum‐classical transition of physical systems in complex space.