{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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 (
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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 ]....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern