I The free particle in spherical coordinates

loewenzahn
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the free particle in spherical coordinates
Hi!
I'm studying Shankar's Principle of quantum mechanics
I didn't get the last conclusion, can someone help me understand it, please. Where did the l over rho come from?

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Expand the 2nd line. (And btw, if you still don't get it, show your attempt.)
 
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Likes vanhees71 and Nugatory
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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