TITLE:
About an Ambiguity Appearing on the Hamiltonian Formulation of Quantum Mechanics
AUTHORS:
Gustavo V. López, Ana Griselda, Carlos R. Martínez-Prieto
KEYWORDS:
Harmonic Oscillator, Quantum Bouncer, Ambiguities in Quantum Mechanics Theory
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.6,
June
28,
2018
ABSTRACT: 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.