Schrödinger's equation from Snell's law
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Schrödinger's equation from Snell's law. / Lima, Nathan; Karam, Ricardo.
I: European Journal of Physics, Bind 43, Nr. 3, 035402, 2022.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Schrödinger's equation from Snell's law
AU - Lima, Nathan
AU - Karam, Ricardo
N1 - Publisher Copyright: © 2022 European Physical Society.
PY - 2022
Y1 - 2022
N2 - A new derivation of Schrödinger's equation is presented, based on Schrödinger's original discussions on refraction and the optical-mechanical analogy, but adopting a much simpler formalism: Newtonian mechanics and some basic elements of classical wave theory (such as Snell's law). We compare how particles and waves refract and show that the 'law of particle refraction' and the 'law of wave refraction' may become consistent if one assumes that a particle can be represented by a wave group. In this case, the differential equation whose solutions represent the waves forming such wave group is the Schrödinger equation. Due to the simplicity of the adopted mathematical formalism, we argue that this derivation can be used in quantum mechanics courses at introductory level to give students an idea of Schrödinger's original path to his wave equation.
AB - A new derivation of Schrödinger's equation is presented, based on Schrödinger's original discussions on refraction and the optical-mechanical analogy, but adopting a much simpler formalism: Newtonian mechanics and some basic elements of classical wave theory (such as Snell's law). We compare how particles and waves refract and show that the 'law of particle refraction' and the 'law of wave refraction' may become consistent if one assumes that a particle can be represented by a wave group. In this case, the differential equation whose solutions represent the waves forming such wave group is the Schrödinger equation. Due to the simplicity of the adopted mathematical formalism, we argue that this derivation can be used in quantum mechanics courses at introductory level to give students an idea of Schrödinger's original path to his wave equation.
KW - quantum theory
KW - Schrödinger equation
KW - Snell's law
KW - wave mechanics
U2 - 10.1088/1361-6404/ac5635
DO - 10.1088/1361-6404/ac5635
M3 - Journal article
AN - SCOPUS:85127570760
VL - 43
JO - European Journal of Physics
JF - European Journal of Physics
SN - 0143-0807
IS - 3
M1 - 035402
ER -
ID: 303450484