Time dependent perturbation theory

jc09
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Hi I was wondering if someone could help me out. I have been studying TDPT and was wondering how it applies to atomic physics or if someone could give me a example that would be great.
 
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The usual example given for TDPT is stimulated emission. You put a hydrogen atom which is in an excited state, and see that a time-varying electric-field perturbation will cause that hydrogen atom to spontaneously decay to a lower energy state, and therefore emit a photon.
 
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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