CRC Press eBooks

Linear Algebra for Quantum Mechanics

Caio Lima Firme

Published Mar 21, 2022• 0 citations

Abstract

Matrices, vectors and determinants are presented in this chapter, mainly their applications to the quantum mechanics and quantum chemistry. A very important property of the matrices is that they do not commute and this leads to the commutator relations discussed in the end of this chapter and to most important features of the quantum matrix mechanics, for example, the uncertainty principle. In this chapter, the most important properties of the matrices (trace of matrix, matrix multiplication, transpose of a matrix, symmetric and orthogonal matrix) are shown along with the methods to obtain the determinant of the matrix (Gaussian elimination and Laplace expansion). The Gauss-Jordan method to obtain the inverse matrix is presented and antissymetric matrices and its importance to quantum mechanics. Matrix diagonalization, Jacobi method of diagonlization, eigenvectors in vector space, Hermitian matrix, unitary transformation and linear transformations, characteristic equations and system of secular homogeneous linear equations are shown in sequence which are vital for several operations in the quantum wave mechanics. Several Fortran codes of linear algebra are also displayed in this chapter (174 words).

DOI: 10.1201/9781003050582-4

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