Why Does My Emission Spectra Prediction Program Differ from Lab Results?

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Hi there. I'm new to this board so please excuse if this is misplaced, there seems to be too many places to choose from.

While browsing my computer I found a little program I wrote when doing year 12 physics that was based on the textbook material about ionization energies. It recurssively calculates possible 'electron jumps' between energy levels and approximately displays the visible portion of the resulting photons. You can download it http://www.heraldsofdeath.com/geargod/downloads/freq.exe . It will ask for a number of electrons and for each one, the ionization energy required. It will then ask the recurssion depth, think of this as the 'temperature' to which the 'sample' is heated.

The program has no trouble calculating hydrogen and several other atoms if I remember right, but for other atoms the output is very different from lab results. Could someone explain to me why this is the case? I'm afraid that I have not touched physics since then and if anything, got stupider over the time.
 
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What kind of an calculational scheme did you use? Since it was based on a grade 12 textbook I really doubt it was too realistic. To get accurate results you'd have to consider screening and electron-electron correlation effects for example. Every electron in an atom interacts with the others via quantum mechanical effects and the Coulomb interaction and that makes atoms very complex systems. You probably got the best results with hydrogen-like atoms because... well because they're hydrogen-like and it's the simplest possible atom.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
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