About an Ambiguity Appearing on the Hamiltonian Formulation of Quantum Mechanics

作     者：Gustavo V. López Ana Griselda Carlos R. Martínez-Prieto 

作者机构：Departamento de Física Universidad de Guadalajara Guadalajara Mexico 

出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)

年 卷 期：2018年第6卷第6期

页      面：1382-1387页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Harmonic Oscillator Quantum Bouncer Ambiguities in Quantum Mechanics Theory 

摘      要：We study classical and quantum dynamics of the symmetric harmonic oscillator and the symmetric bouncer defined in 2-D. For these systems we get each of them for two different constants of motion, two Lagrangians and two Hamiltonians which describe the same classical dynamics. However, the quantization of these systems (using Schrödinger equation), using their two equivalents Hamiltonian, describes different quantum dynamics for each of them. This represents an ambiguity on the Hamiltonian formulation of the Quantum Mechanics.