An Approach to Construct Wave Packets with Complete Classical-Quantum Correspondence in Non-relativistic Quantum Mechanics |
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Authors: | Pouria Pedram |
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Institution: | (1) Plasma Physics Research Center, Science and Research Campus, Islamic Azad University, Tehran, Iran |
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Abstract: | We introduce a method to construct wave packets with complete classical and quantum correspondence in one-dimensional non-relativistic
quantum mechanics. First, we consider two similar oscillators with equal total energy. In classical domain, we can easily
solve this model and obtain the trajectories in the space of variables. This picture in the quantum level is equivalent with
a hyperbolic partial differential equation which gives us a freedom for choosing the initial wave function and its initial
slope. By taking advantage of this freedom, we propose a method to choose an appropriate initial condition which is independent
from the form of the oscillators. We then construct the wave packets for some cases and show that these wave packets closely
follow the whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm interpretation of quantum mechanics
to quantify this correspondence and show that the resulting Bohmian trajectories are also in complete agreement with their
classical counterparts. |
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Keywords: | Schr?dinger equation Classical-quantum correspondence Wave packets |
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