Proof of the variational principle
Not what you're looking for?
Show that the average of the Hamiltonian is an upper bound to the ground state energy.
Purchase this Solution
Solution Summary
We give a proof of the variational principle for the ground state energy.
Solution Preview
Let |psi_n> be the normalized eigenstates with eigenvalue E_n of the Hamiltonian H:
H|psi_n> = E_n |psi_n> (1)
If |psi> is any arbitrary state we can always expand it in terms of the eigenstates:
|psi> = sum from n = 0 to infinity of c_n |psi_n> (2)
The expansion coefficients c_n are given by:
c_n = <psi_n|psi>
If |psi> is normalized then:
<psi|psi> =1
Inserting (2) in here and using that |psi_n> are orthonormal ...
Purchase this Solution
Free BrainMass Quizzes
Variables in Science Experiments
How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.
Classical Mechanics
This quiz is designed to test and improve your knowledge on Classical Mechanics.
Basic Physics
This quiz will test your knowledge about basic Physics.
Introduction to Nanotechnology/Nanomaterials
This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.
Intro to the Physics Waves
Some short-answer questions involving the basic vocabulary of string, sound, and water waves.