學習資源量子化學課件2012

1、Operators and their finite matrix representationslinear algebra, differential and integral calculusReference:A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover Publications, Inc., New York, 1996Chapter 1The HamiltonianWe will introduce s

2、uitable mathematical machinery to solve the equationKey mathematical pointsBasis, delta functionOperators and matrix representationThe representations between different bases are mutually relatedProperties of determinants The variational method is the most powerful mathematical tool in QMMathematica

3、l machineryVectorsMatricesOrthogonal functionsOperatorsThe variation methodNotations: linear algebra, differential and integral calculus1.1 Linear algebraSupplementary MaterialSupplementary Materials(a determinant is invariant w.r.t. the unitary transformation of the matrix)All the above shows that

4、an operator is equivalent to its matrix representation ina complete basis. The spectral resolution isSummary: Discretization of an operatorIf we have a complete basisifSupplementary MaterialsSupplementary MaterialsGiven thatthe matrix element of reads Or in Dirac notationWe can use these relations to solve the following set of inhomogeneous linear systemof equations:Choose to makeSummary: mathematical machineryBasis, delta functionOperators and matrix representationThe representations between different bases are mutually relatedProperties of dete