Explain Energy Level Split for Two Atoms

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Energy level splitting in a two-atom system, such as two copper atoms, results in a combined system with 58 electrons instead of 28. Each energy level of the isolated atom splits into two levels to accommodate the increased number of electrons. For example, the 1s subshell, which normally holds 2 electrons, can now hold 4 electrons due to this splitting. This allows for proper filling of the electrons in the sub-shells of the two-atom system. Understanding this concept is crucial for grasping the behavior of multi-atom systems in quantum mechanics.
anhnha
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Hi,
can anyone help me explain more detail about energy level split with the system of two atoms?
Please see this video at 06:32:http://www.youtube.com/watch?v=y_GZn4o8gaE
Thank you.
 
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Haha, I have just seen the answer:
Consider 2 atoms of copper. So now we will think of this as a single two-atom system and not as a system with 2 atoms in it. This system now has 58 electrons(not 28 electrons in two atoms). How do we fill these electrons in the sub-shells?The 1s subshell can only accommodate 2 electrons. But we want that it should have 4 e's. So each energy level of the isolated atom splits into two levels for the two-atom system. Thus 4 e's can now be accommodated in the two levels of the 1s sub-shell.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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