How Would Solving Schrodinger and Dirac Equations Analytically Impact Science?

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What would be the foreseeable impacts on science if it were possible to solve the Schrodinger or even Dirac equations analytically (and exactly) for every case?
 
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It can't be done, so this sounds like pointless speculation.
 
DrClaude said:
this sounds like pointless speculation.

Indeed. Thread closed.
 
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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