| S.H. Patil and K.T. Tang
Asymptotic Methods in Quantum Mechanics, Applications to Atoms, Molecules and Nuclei
This book describes some general properties of wave functions, with an emphasis on their asymptotic behavior. The asymptotic region is particularly important since it is the wave function in the outer region of an atom, a molecule or a nucleus, which is sensitive to external interaction. An analysis of these properties helps in construction simple and compact wave functions and in developing a broad understanding of different aspects of the quantum mechanics of many partic e systems. As applications, wave functions with correct asymptotic forms are used to generate a large data base for susceptibilities, polarizabilities, interatomic potentials, and unclear densities.
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations, and variational methods are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problems with answers are used to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.
- Mathematical Methods for Engineers and Scientists 1
Complex Analysis, Determinants and Matrices
- Mathematical Methods for Engineers and Scientists 2
Vector Analysis, Ordinary Differential Equations and Laplace Transforms
- Mathematical Methods for Engineers and Scientists 3
Fourier Analysis, Partial Differential Equations and Variational Methods