2017/08/30 by J. F. Ogilvie, Ogilvie, J. F.
Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1709.04759
openalex publication_date 2017/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A partial separation of the variables is practicable for the solution of Schroedinger's temporally independent equation in cartesian coordinates x,y,z, which yields moderately simple algebraic formulae for the amplitude functions involving quantum numbers k,l,m, the same as in spherical polar coordinates. The properties of angular momentum are thus achieved with no angular variable. Several plots of surfaces of constant psi(x,y,z) are presented to illustrate the resemblance of the shapes of these surfaces to the shapes of surfaces of psi(r,theta,phi) with the corresponding quantum numbers.