1
vote
0answers
61 views

Variational principle

In the LMTO method, the interstitial region is approximated by plane waves and the muffin tin region of the potential by solutions to the radial Schrodinger equation. In using the variational method ...
7
votes
1answer
204 views

Virial theorem and variational method: a question

I have an hydrogenic atom, knowing that its ground-state wavefunction has the standard form $$ \psi = A e^{-\beta r} $$ with $A = \frac{\beta^3}{\pi}$, I have to find the best value for $\beta$ ...
9
votes
1answer
1k views

Variational Derivation of Schrodinger Equation

In reading Weinstock's Calculus of Variations, on pages 261 - 262 he explains how Schrodinger apparently first derived the Schrodinger equation from variational principles. Unfortunately I don't ...
2
votes
0answers
305 views

Prove that the first order perturbation theory overestimates fundamental state [closed]

This was a question on my exam and I don't know how to solve it. Use the variational principle to prove that the first order perturbation theory always overestimates the energy of the fundamental ...
1
vote
0answers
168 views

Are there any good reading materials for variational approach in many-body theory? [closed]

I need something like a summary of existing results, including the treatment of BCS Hamiltonian and Hubbard model. Auerbach's book is a good one but I still hope to get more comprehensive review. My ...
4
votes
1answer
140 views

Variational wavefunctions and “spread” of potential in quantum mechanics

A particle in a box has an energy that decreases with the size of the box. In the general case, it is often said that a variational solution for a "narrow and deep" potential is higher in energy than ...
25
votes
5answers
2k views

Hamilton's Principle

Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum). Why should the action integral be stationary? On ...