Calculating Energies of 1D Quantum Harmonic Oscillator with Artificial Neural Networks

Nieto-Chaupis H. · International Conference on Engineering and Emerging Technologies, ICEET (2025) · DOI: 10.1109/iceet67911.2025.11424047

Resumen

We employ the simplest representation of perceptron and orthogonal polynomials, to derive the quantized energies of an one-dimension harmonic oscillator by using mathematical methodologies that are interpreted in terms of quantum language. In contrast to standard mechanisms based in the usage of annihilation and creation operators, the oscillator turns out to be quantized. Indeed, a generalization is presented, fact that might be interpreted as a path to quantize 2D and 3D oscillators. From the Schrödinger equation, the respective solution namely the wave function for present case is also estimated in a closed-form. In the present case, the well-known integer-order Bessel functions are employed. The resultant energy spectra are in agree with quantum mechanics calculations.

Instituciones: Universidad Autónoma del Perú