Mastering the Operator: Unlocking Its Purpose and Benefits

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can anyone help me to understand the operator and what's the goal to study it?
 
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The is no such thing as"the operator". In mathematics there is a subject called operator theory, while in physics there are different operators in different contexts.
 


i mean the operators in Quantum Mechanics (Hermiticity)
 
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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