Understanding Time-Independent Schrodinger Equation

saravanan13
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In quantum mechanics, time independent Schrodinger equation gives dynamics of system.
How do one claim that this equation is evolution of a system? Since dynamics need time dependency. How do one explain this discrepancy?
Thanks in well advance...
 
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It's actually the time dependent SE that gives the dynamics. It just turns out that solving the time dependent SE is accomplished by first solving the time independent version, and then the associated time dependence that comes from the time dependent version is rather trivial to attach to the eigenstates of the time independent version.
 
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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