Power Curves

Power curves using both an approach from Quantum physics and an approach from Semi-Classical physics to demonstrate Bohr’s correspondence principle—based on Jasper’s thesis.

Mathematica Files for Power Curves

Main Mathematica file that contains everything **Use This for paper**: Master Document


Quantum vs Semi-Classical power curves: Combined Quantum and Semi Classical Approaches Plot

Comparison of the Semi-Classical approaches used in Jasper’s thesis and Horbatsch’s paper: SemiClassical Power Curve Jasper vs Horbatsch Comparison

Comparison of the Quantum approaches used in Jasper’s thesis and Horbatsch’s paper: Quantum Power Curve Jasper vs Horbatsch Comparison

Comparison of Horbatsch’s Semi-Classical scaled and unscaled approaches with Jasper’s Quantum one: Horbatsch vs HorbatschScaledBinnedSums

Binned sums of scaled curve: BinnedSums

Graphs and Images:

Binned plots pdfs from n=100 l=10-90: Binned power curve graphs-20230731T192151Z-001

Pavel’s quantum vs semi-classical graphs: Pavel’s power curve graphs-20230804T191537Z-001

Animation of Electron Orbiting Nucleus Hydrogen Atom (with nucleus at origin now): Elliptical Animation


Jasper Arnold Princeton Senior Thesis: Jasper Thesis Final

Jackson textbook problem, pg 502: Jackson pg 502

M. W. Horbatsch, E. A. Hessels, and M. Horbatsch: Classical calculation of the lifetimes and branching ratios for radiative decays of hydrogenic atoms

G. S. Khandelwal and E. E. Fitchard Paper: The Square of the Radial Integral for Calculating the Dipole Oscillator Strengths for Transitions in Hydrogen Atoms in their 3(3, p, OR d) and 4(>, p, d, OR/) States

Charlotte E. Moore’s Tables: Selected Tables of Atomic Spectra

W. L. Wiese’s, M. W. Smith’s, and B. M. Glennon’s Tables: Atomic Transition Probabilities Volume I through Neon

Pavel’s code and tables: Pavel’s Code-20230804T191553Z-001





Stark Effect

Google Sheet file that simulates an electron orbit in a hydrogen atom using the Hamiltonian:


Mathematica program:

Graph Elliptical Orbit From Hamiltonian.nb

Python Program:



Work by David Litman and Roshan Natarajan