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Unformatted text preview: PHYS 385 Lecture 33 - Molecules II 33 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 33 - Molecules II What's important : • variational approach to molecular states • LCAO - linear combination of atomic orbitals Text : Gasiorowicz, Chap. 20 H 2 + molecular ion (cont'd) In the previous lecture, we started with a Hamiltonian for the H 2 + molecular ion reading H = -( h 2 /2 m A ) ∇ A 2- ( h 2 /2 m B ) ∇ B 2- ( h 2 /2 m e ) ∇ e 2- ke 2 / r A- ke 2 / r B + ke 2 / R AB . (1) The first approximation we invoked to help solve this was the Born-Oppenheimer approximation, which regards the nuclei as fixed compared to the motion of the electrons. Thus, in the B-O approximation: H ≅- ( h 2 /2 m e ) ∇ e 2- ke 2 / r A- ke 2 / r B at fixed R AB . (2) To actually solve this approximate Hamiltonian, we ’ ll make use of a technique called the Variation Principle , which states: Given any approximate wavefunction satisfying the boundary conditions of the problem, the expectation value of the energy calculated from this function will always be higher than the true energy of the ground state. The strategy is the following: (a) select a set of wavefunctions (educated guess) which best resemble the true wavefunction (b) calculate the energy < E > as a function of a set of coefficients representing the...
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This note was uploaded on 09/07/2009 for the course PHYS 385 taught by Professor Davidboal during the Spring '09 term at Simon Fraser.
- Spring '09
- Quantum Physics