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## Main Question or Discussion Point

Hi,

I'm interested in learning about what would be the compliment to the Variational method. I'm aware that the Variational method allows one to calculate upper bounds, but I'm wondering about methods to calculate lower bounds on energy eigenvalues. And for energies besides the ground state if such methods exist.

Are there methods to calculate lower bounds on energy eigenvalues (the ground state and higher)?

Thanks,

I'm interested in learning about what would be the compliment to the Variational method. I'm aware that the Variational method allows one to calculate upper bounds, but I'm wondering about methods to calculate lower bounds on energy eigenvalues. And for energies besides the ground state if such methods exist.

Are there methods to calculate lower bounds on energy eigenvalues (the ground state and higher)?

Thanks,