CRC Press eBooks

The Schrödinger Equation

Ram Yatan Prasad, Pranita

Published Jan 15, 2021• 0 citations

Abstract

The sixth chapter begins with the equation of wave motion in one dimension and arrived at the three-dimensional Laplacian operator. After this, time-independent and time-dependent Schrödinger’s equations have been derived in a simple way. It also deals with the interpretation of wave function and mentions the conditions of acceptable wave functions taking into consideration the graphical presentation. This chapter also gives idea about the condition of normalisation and orthogonality and determination of normalisation constant. The condition of orthogonality has also been discussed in detail, which gives an important point regarding how two wave functions become orthogonal. It also speaks about orthonormality. The ideas of Eigen function and Eigen value have also been introduced, and degeneracy has been defined. This chapter also incorporates the transformation of Laplacian operator into spherical polar coordinates in a graspable manner. The Ehrenfest theorem and its proof have also been included. The chapter also provides the idea of matrix representation of wave function, matrix representation of operator, properties of matrix elements, and matrix form of time-dependent Schrödinger equations. At the end of the chapter, adequate references, solved problems, and questions on concepts have also been cited.

DOI: 10.1201/9781003133605-6

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