TY - JOUR

T1 - Did Schrödinger have other options?

AU - Grave De Peralta, Luis

N1 - Publisher Copyright:
© 2020 European Physical Society.

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - history of science

KW - philosophy of science

KW - quantum mechanics

KW - relativistic wave equations

UR - http://www.scopus.com/inward/record.url?scp=85089913837&partnerID=8YFLogxK

U2 - 10.1088/1361-6404/aba7dc

DO - 10.1088/1361-6404/aba7dc

M3 - Article

AN - SCOPUS:85089913837

VL - 41

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 6

M1 - 065404

ER -