Did Schrödinger have other options?

Wave mechanics triumphed when Schrödinger published his now famous equation and showed how to describe hydrogen-like atoms using it. However, while looking for the right equation, Schrödinger first explored, but did not publish, the equation that we today call the Klein–Gordon equation. An alternative possible choice is explored in this work. It is shown a quasi-relativistic wave equation which solutions match the Schrödinger's results at electron energies much smaller than the energy associated to the electron's mass, but include, at higher energies, the relativity energy's correction calculated in traditional first order perturbation theory. A discussion is presented about several consequences that would follow from using this quasi-relativistic wave equation as a quantum mechanics foundational equation. It is also suggested the academic use of this equation for introducing the students to the implications of the special theory of relativity in introductory quantum mechanics courses. (paper)