1. ### I Using the Variational Method to get higher sates

In a typical quantum course we learn how to approximate the ground state of a particular Hamiltonian by making an educated guess at an ansatz with a tunable parameter then calculating the expectation energy for the ansatz. The result will depend on the tunable parameter if done correctly. Then...
2. ### A Lagrangian to the Euler-Lagrange equation

Hello all, I understand the formation of the Lagrangian is: Kinetic Energy minus the potential energy. (I realize one cannot prove this: it is a "principle" and it provides a verifiable equation of motion. Moving on... One inserts the Lagrangian into the form of the "Action" and minimizes it...
3. ### Deriving geodesic equation using variational principle

I am trying to derive the geodesic equation using variational principle. My Lagrangian is $$L = \sqrt{g_{jk}(x(t)) \frac{dx^j}{dt} \frac{dx^k}{dt}}$$ Using the Euler-Lagrange equation, I have got this.  \frac{d^2 x^u}{dt^2} + \Gamma^u_{mk} \frac{dx^m}{dt} \frac{dx^k}{dt} =...
4. ### DFPT second order energy variational form

I am referring to perturbation expansion of density functional Kohn Sham energy expression in Phys. Rev. A 52, 1096. In equation (92) the variational form of the second order energy is listed, but I cannot seem to work out the last 3 terms involving XC energy and density. Particularly, the...
5. ### Lower bounds on energy eigenvalues

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...