How is Hamiltonian energy of orbital differ from orbital in certain

boodyx1
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how is Hamiltonian energy of orbital differ from orbital in certain atom with another atom although the two orbital have the same no. of electrons...
ex...Hamiltonian energy differ in lithium and hydrogen although both have one electron in last orbital
please help me quickly
 
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lol, just curious, why the rush? ;]

Well these 2 atoms you mention have nothing in common. They have different atomic number, which means the potential V (that gets in schrodinger equation) is different which finally means that you'll get different Hamiltonian eigenstates (energies)
 


r u trust in this answer...and how the atomic no. can change in V
 
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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