#variationalMethod #groundstateenergy #hydrogenmoleculeion
Lecture Notes:
Board Image:
In this lecture, we explore the hydrogen molecule ion (H2+), a fundamental system in quantum mechanics and molecular physics. Using the variational principle, we analyze how a single electron behaves in the Coulomb field of two protons fixed at a distance R.
We begin by constructing the Hamiltonian for the system, applying the Born-Oppenheimer approximation, and formulating a trial wave function using the Linear Combination of Atomic Orbitals (LCAO) technique. The lecture discusses the normalization of the wave function and the concept of the overlap integral, providing key insights into molecular bonding and stability.
This discussion not only introduces an essential application of quantum mechanics but also highlights the methods used to determine whether the hydrogen molecule ion forms a stable bond. Perfect for students studying quantum chemistry, molecular physics, and variational methods in quantum mechanics!
Topics Covered:
Variational principle and molecular bonding
Hamiltonian of H2+ and the Born-Oppenheimer approximation
Constructing and normalizing the trial wave function
Overlap integral and its significance.