How is there discrepancy between GR and QM?

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I watched The Elegant Universe, and it was somewhat disappointing. At the current moment, I only know some of the math of SR, no math of GR, and no math of QM. The special kept giving vague overviews of why GR and QM don't mix. I do know some of the concepts for GR and QM, and I do not see why they would conflict, or how they would conflict as they cover different territories. GR deals with mass, Qm deals with everything else. Would somebody give me an example of a problem where GR and QM give different results, so I can understand what the fuss is about? Thanks.
 
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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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