Variational Theory: Ground vs Non-Ground States

[greisen]

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

 

[Gokul43201]

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.

 

[greisen]

okay thanks for the answer