Determining the accuracy of the Variational Method

[joel31]

The Variational Method allows us to obtain an upper bound on energy of the ground state (and sometimes excited states).

Is there any way of determining an upper bound on the error of the energy obtained by the variational method without an analytic or numerical solution to the problem?

i.e. Is there any way of knowing how close our resulting energy is to the true ground state energy?

 

[hilbert2]

In addition to the variational method for finding an upper bound for the energy, there are some ways to determine a lower bound for the ground state energy, as is described here: https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.21297

Then you can set the estimate of ground state energy to be the average of the upper and lower bounds and the error bars are obvious.