Solution of the hydrogen atom using Supersymmetry

In this work we present the solution of the Schrödinger equation through a modern version of the factorization method by using the formalism of the so-called Supersymmetric Quantum Mechanics. The analyzed system is the hydrogen atom, the radial and the angular parts of the spherical coordinates are studied with the presented methodology. Special emphasis is given to adaptation made to each of these coordinates. The approach used is general and can be presented as an alternative to traditional methods of solution of the Schrödinger equation such as the Frobenius method.

Keywords:
hydrogen atom; supersymmetry; shape invariance; ladder operators; quantum mechanics

Authorship

João Marcos Costa Monteiro ^**Endereço de correspondência: cmonteiro.jm@gmail.com

Universidade Estadual Paulista, Instituto de Biociências, Letras e Ciências Exatas, São José do Rio Preto, SP, BrasilUniversidade Estadual PaulistaBrasilSão José do Rio Preto, SP, BrasilUniversidade Estadual Paulista, Instituto de Biociências, Letras e Ciências Exatas, São José do Rio Preto, SP, Brasil

https://orcid.org/0000-0002-1291-9394

Airton Algozini Júnior

Elso Drigo Filho

^*Endereço de correspondência: cmonteiro.jm@gmail.com

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Tables | Formulas

Tables (1)
Formulas (87)

j	l	m	$P_{l}^{m} (c o s θ) [2]$	$Θ_{j} (θ; l)$
0	0	0	1	1
0	1	1	$s e n (θ)$	$s e n (θ)$
0	2	2	$3 s e n^{2} (θ)$	$s e n^{2} (θ)$
0	3	3	$15 s e n (θ) [1 - \cos^{2} (θ)]$	$s e n^{3} (θ) = s e n (θ) [1 - \cos^{2} (θ)]$
1	1	0	$cos (θ)$	$cos (θ)$
1	2	1	$3 s e n (θ) \cos (θ)$	$s e n (θ) \cos (θ)$
1	3	2	$15 s e n^{2} (θ) cos (θ)$	$s e n^{2} (θ) cos (θ)$