Relationship between Wave Packet Wavelength & Group Velocity

yellowgold
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What is the relationship wavelength and group velocity in wave packet ? If a wave packet has big wavelength its group velocity bigger or not ?
 
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yellowgold said:
What is the relationship wavelength and group velocity in wave packet ? If a wave packet has big wavelength its group velocity bigger or not ?

If you know the definition of group velocity you can do this by yourself as an exercise. Recall the relation between (de Broigle) wavelenght v.s momentum and then you have it.
 
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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