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.
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机译:国际研究会"New Development of Numerical Simulation in Low-Dimensional Quantum Systems:From Density Matrix Renormalization Group to Tensor Network Formulation"(研究会报告)