Perturbation Theory for Atomic and Molecular Properties
- 60 Downloads
Perturbation theory is the most general and systematic technique for the approximate solution of quantum-mechanical eigenvalue problems. It is assumed that the eigenproblem for some model problem that affords a reasonable zero-order approximate solution to the problem of interest can be solved exactly. A perturbation, H 1, is added to the zero-order Hamiltonian, H 0, associated with the model problem, in order to recover the full Hamiltonian for the system, H. A parameter, λ, is introduced in the Hamiltonian, H= H 0 + λH 1, so as to interpolate between the zero-order Hamiltonian, λ = 0, and the full Hamiltonian, λ = 1. By making expansion in powers of λ for the exact energy and the exact wave function, and then equating the coefficients for each power of λ, a set of equations can be obtained which are then employed to obtain corrections to the zero-order energy and wave function.
KeywordsPerturbation Theory Algebraic Expression Principal Term Energy Coefficient Perturbation Operator
Unable to display preview. Download preview PDF.
- 2.E. C. Kemble, The Fundamental Principles of Quantum Mechanics, McGraw-Hill, New York (1937); Dover, New York (1958).Google Scholar
- 3.L. Pauling and E. B. Wilson, Introduction to Quantum Mechanics, McGraw-Hill, New York (1935).Google Scholar
- 4.P. A. M. Dirac, The Principles of Quantum Mechanics, Clarendon Press, Oxford (1958).Google Scholar
- 6.J. O. Hirchfelder, W. Byers Brown, and S. Epstein, Adv. Quant. Chem. 1, 266 (1964).Google Scholar
- 8.S. Wilson, Electron Correlation in Molecules, Clarendon Press, Oxford (1984).Google Scholar