Mathematical methods in science and engineering / by Selçuk Şükrü Bayin.

Online resource; title from PDF title page (EBSCO, viewed March 5, 2018)

Includes bibliographical references and index.

'l 149 8.6.2 Construction of the Eigenfunctions 150 8.6.3 Ladder Operators for m 151 8.6.4 Interpretation of the L+ and L− Operators 153 8.6.5 Ladder Operators for l 155 8.6.6 Complete Set of Ladder Operators 159 8.7 Schrödinger Equation and Single-Electron Atom (Type F) 160 8.8 Gegenbauer Functions (Type A) 162 8.9 Symmetric Top (Type A) 163 8.10 Bessel Functions (Type C) 164 8.11 Harmonic Oscillator (Type D) 165 8.12 Differential Equation for the Rotation Matrix 166 8.12.1 Step-Up/Down Operators for m 166 8.12.2 Step-Up/Down Operators for m′ 167 8.12.3 Normalized Functions with m = m′ = l 168 8.12.4 Full Matrix for l = 2 168 8.12.5 Step-Up/Down Operators for l 170 Bibliography 171 Problems 171 9 Coordinates and Tensors 175 9.1 Cartesian Coordinates 175 9.1.1 Algebra of Vectors 176 9.1.2 Differentiation of Vectors

Eigenfunctions 123 7.4.3 Completeness and the ExpansionTheorem 123 7.5 Generalized Fourier Series 125 7.6 Trigonometric Fourier Series 126 7.7 Hermitian Operators in Quantum Mechanics 127 Bibliography 129 Problems 130 8 Factorization Method 133 8.1 Another Form for the Sturm–Liouville Equation 133 8.2 Method of Factorization 135 8.3 Theory of Factorization and the Ladder Operators 136 8.4 Solutions via the Factorization Method 141 8.4.1 Case I (m > 0 and '(m) is an increasing function) 141 8.4.2 Case II (m > 0 and '(m) is a decreasing function) 142 8.5 Technique and the Categories of Factorization 143 8.5.1 Possible Forms for k(z, m) 143 8.5.1.1 Positive powers of m 143 8.5.1.2 Negative powers of m 146 8.6 Associated Legendre Equation (Type A) 148 8.6.1 Determining the Eigenvalues,

Legendre equation and polynomials -- Laguerre polynomials -- Hermitepolynomials -- Gegenbauer and Chebyshev polynomials -- Bessel functions -- Hypergeometric functions -- Sturm-Liouville theory -- factorization method -- Coordinates and tensors -- Continuous groups and representations -- Complex variables and functions -- Complex integrals and series -- Fractional calculus -- Infinite series -- Integral transforms -- Variational analysis -- Integral equations -- Green's functions -- Green's functions and path integrals.