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Matrix Mechanics

# Matrix Mechanics - will be infinite if we actually have a...

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Matrix Mechanics As we mentioned previously in section 2 , Heisenberg's matrix mechanics, although little-discussed in elementary textbooks on quantum mechanics, is nevertheless formally equivalent to Schrödinger's wave equations. Let us now consider how we might solve the time-independent Schrödinger equation in matrix form. If we want to solve as a matrix problem, we need to find a suitable linear vector space. Now is an -electron function that must be antisymmetric with respect to interchange of electronic coordinates. As we just saw in the previous section, any such -electron function can be expressed exactly as a linear combination of Slater determinants, within the space spanned by the set of orbitals . If we denote our Slater determinant basis functions as , then we can express the eigenvectors as (195) for possible N-electron basis functions (
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Unformatted text preview: will be infinite if we actually have a complete set of one electron functions ). Similarly, we construct the matrix in this basis by . If we solve this matrix equation, , in the space of all possible Slater determinants as just described, then the procedure is called full configuration-interaction , or full CI. A full CI constitues the exact solution to the time-independent Schrödinger equation within the given space of the spin orbitals . If we restrict the -electron basis set in some way, then we will solve Schrödinger's equation approximately . The method is then called ``configuration interaction,'' where we have dropped the prefix ``full.'' For more information on configuration interaction, see the lecture notes by the present author [ 7 ] or one of the available review articles [ 8 , 9 ]....
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