2021/08/25 by J. C. Morales, Morales, Juan C., Carlos A. Arango +2
Physics and Astronomy · #Mechanical and Optical Resonators #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2108.11487
Employing the phase-space representation of second order ordinary\ndifferential equations we developed a method to find the eigenvalues and\neigenfunctions of the 1-dimensional time independent Schr "odinger equation for\nquantum model systems. The method presented simplifies some approaches shown in\ntextbooks, based on asymptotic analyses of the time-independent Schr "odinger\nequation, and power series methods with recurrence relations. In addition, the\nmethod presented here facilitates the understanding of the relationship between\nthe ordinary differential equations of the mathematical physics and the time\nindependent Schr "odinger equation of physical models as the harmonic\noscillator, the rigid rotor, the Hydrogen atom, and the Morse oscillator.\n