Phase-space matrix representation of differential equations for
obtaining the energy spectrum of model quantum systems
- URL: http://arxiv.org/abs/2108.11487v1
- Date: Wed, 25 Aug 2021 21:59:16 GMT
- Title: Phase-space matrix representation of differential equations for
obtaining the energy spectrum of model quantum systems
- Authors: Juan C. Morales and Carlos A. Arango
- Abstract summary: We develop a method to find the eigenvalues and eigenfunctions of the 1-dimensional time independent Schr"odinger equation for quantum model systems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Employing the phase-space representation of second order ordinary
differential equations we developed a method to find the eigenvalues and
eigenfunctions of the 1-dimensional time independent Schr\"odinger equation for
quantum model systems. The method presented simplifies some approaches shown in
textbooks, based on asymptotic analyses of the time-independent Schr\"odinger
equation, and power series methods with recurrence relations. In addition, the
method presented here facilitates the understanding of the relationship between
the ordinary differential equations of the mathematical physics and the time
independent Schr\"odinger equation of physical models as the harmonic
oscillator, the rigid rotor, the Hydrogen atom, and the Morse oscillator.
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