Quantum Physics

    

Schrödinger’s Equation in Non-Euclidean Metric Using Geometric Algebra

Authors: Jesús Sánchez

In this paper, it is used geometric algebra to derive the Schrödinger equation in non-Euclidean metric. The properties of the basis vectors transporting information of the metric, will be used for this goal.The result for the time dependent Schrödinger’s equation is:(ℏt ̂)/g_tt ∂ψ/∂t= -ℏ^2/2m g_tt/〖g_xx〗^2 ((∂^2 ψ)/(∂x^2 )+(∂^2 ψ)/(∂y^2 )+(∂^2 ψ)/(∂z^2 ))+Vψ (1) And for the time independent equation: g_tt (1/〖g_xx〗^2 (∂^2 ψ)/(∂x^2 )+1/〖g_yy〗^2 (∂^2 ψ)/(∂y^2 )+1/〖g_zz〗^2 (∂^2 ψ)/(∂z^2 ))+2m/ℏ^2 (E-V)ψ=0 (2)Being gii, the corresponding metric elements of each coordinate. Also, other possibilities that offer geometric algebra to work in Quantum Mechanics will be commented.

Comments: 15 Pages.

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Submission history

[v1] 2022-08-18 09:29:07

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