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 -