Questions about operators in QM

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helow guys i am atif elahi from pakistan i have some problem in topic operators in quantum mechanics can you people help me
i shall be very thankful to you thanks
 
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If you have general questions, please feel free to post them. If you have questions about homework exercises or assignments, please post them in the Homework & Coursework Questions section here on PF, probably in the Advanced Physics forum.

I see that in other threads you've tried to ask for help via e-mail. I deleted those postings because they're basically duplicates of this one. I think most people here would rather discuss questions publically, so that other people who read this forum can benefit from the discussion. Also, if the discussion is public, you get the benefit of "peer review" of the answers. Other people can post corrections if they think there are mistakes.
 
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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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