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We describe the state of electrons inside specific orbitals:

We assign each orbital a number from 0,1,2... In each orbital each electron has a specific energy level E_0,E_1,E_2,... Electrons in a particular orbital x are in the corresponding quantum state \ket{x}

!Pasted image 20260805145524.png !Pasted image 20260805145536.png

Time evolution of a quantum state

!Pasted image 20260805145615.png

Energy / Hamiltonian

From now on we assume there are only finitely many orbitals N. (not really true)

The total energy of an Electron can be calculated as: !Pasted image 20260805150241.png !Pasted image 20260805150253.png

Schrödingers equation

!Pasted image 20260805151253.png!Pasted image 20260805151259.png