## Selected Mathematical Methods in Theoretical PhysicsSelected Mathematical Methods in Theoretical Physics shows how a scientist, knowing the answer to a problem intuitively or through experiment, can develop a mathematical method to prove that answer. The approach adopted by the author first involves the formulation of differential or integral equations for describing the physical procession, the basis of more general physical laws. Then the approximate solution of these equations is worked out, using small dimensionless physical parameters, or using numerical parameters for the objects under consideration. The eleven chapters of the book, which can be read in sequence or studied independently of each other, contain many examples of simple physical models, as well as problems for students to solve. This is a supplementary textbook for advanced university students in theoretical physics. It will enrich the knowledge of students who already have a solid grounding in mathematical analysis. |

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### Contents

Continual Integrals | 17 |

Calculation of Greens Functions | 33 |

The Whittaker Method | 49 |

Intense Perturbations | 69 |

Inverse Problems | 89 |

The SelfConsistent Approximation | 107 |

Soliton Solutions | 125 |

Dynamic Chaos | 143 |

PreyPredator Population Models | 165 |

Random Processes | 177 |

199 | |

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### Common terms and phrases

according to Eq Analogously angular velocity atom average Bessel function calculate Chapter const constant coordinate correlation function corresponds Coulomb dependence derive determined differential equation diffusion distribution function eigenfunctions eigenvalues electron equal exact example expansion exponent expression follows from Eq Fourier frequency Green's function Hamiltonian harmonic oscillator Hence impact parameter independent variable integral interaction interval large number linear Mathieu equation molecular velocity molecule momentum motion nonlinear notation number of particles obtain one-dimensional pendulum periodic perturbation theory populations of predators potential energy potential U(r previous section prey quantity quantum mechanics quantum number radial random variables region rewrite Reynolds number right side saddle-point method sake of simplicity scattering angle scattering phase scattering potential Schroedinger equation self-consistent approximation separatrice Sine-Gordon equation small compared so-called soliton stationary stochastic Substituting temporal Green's function transition curves transition solutions variation vibrating wall wave function Whittaker WKB approximation Wronskian