Variational Theory: Ground vs Non-Ground States

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The discussion centers on the variational principle in quantum mechanics, specifically addressing the relationship between ground and non-ground states. The ground state, denoted as E_0, is defined as the state with the lowest energy, while non-ground states, represented as E_n, always possess higher energy than E_0. The initial equation presented, (E_n - E_0) >= 0, is clarified as not being a formal statement of the variational principle. Understanding these definitions is crucial for grasping the foundational concepts of quantum mechanics.

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greisen
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Hi,

I am trying to understand the variational principle

(E_n - E_0) >= 0

E_0 is the ground state of the system? E_n is nonground and will the nonground state than always have a higher energy than the ground state?

Thanks in advance
 
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Yes, by definition. The ground sate is defined as the state with lowest energy (i.e., if you know the energy spectrum of a system, you label the lowest energy state as the "ground state").

PS: The equation you wrote above is not a statement of the variational principle.
 
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okay thanks for the answer
 
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