## Problems in Classical and Quantum Mechanics: Extracting the Underlying ConceptsThis book is a collection of problems that are intended to aid students in graduate and undergraduate courses in Classical and Quantum Physics. It is also intended to be a study aid for students that are preparing for the PhD qualifying exam. Many of the included problems are of a type that could be on a qualifying exam. Others are meant to elucidate important concepts. Unlike other compilations of problems, the detailed solutions are often accompanied by discussions that reach beyond the specific problem.The solution of the problem is only the beginning of the learning process--it is by manipulation of the solution and changing of the parameters that a great deal of insight can be gleaned. The authors refer to this technique as "massaging the problem," and it is an approach that the authors feel increases the pedagogical value of any problem. |

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### Contents

Part II Quantum Mechanics | 118 |

A Greek Alphabet | 312 |

B Acronyms Descriptors and Coordinates | 313 |

C Units | 314 |

D Conic Sections in Polar Coordinates | 319 |

E Useful Trigonometric Identities | 322 |

F Useful Vector Relations | 323 |

G Useful Integrals | 324 |

L Useful Formulas | 339 |

M The Infinite Square Well | 342 |

N Operators Eigenfunctions and Commutators | 347 |

O The Quantum Mechanical Harmonic Oscillator | 349 |

P Legendre Polynomials | 351 |

Q Orbital Angular Momentum Operators in Spherical Coordinates | 354 |

R Spherical Harmonics | 357 |

S ClebschGordan Tables | 359 |

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### Common terms and phrases

ˇ ˇ ˇ Ä x Ä a-box angular momentum Appendix approximation atom central potential chapter Classical and Quantum coefficient collision constant cosÂ eigenkets eigenstate eigenvalues electron energy eigenvalues equations of motion evaluate expectation value fine structure constant first-order correction frequency given in Eq ground state energy H-atom Hamiltonian harmonic oscillator integral J.D. Kelley J.J. Leventhal kets kinetic energy L-box ladder operators Lagrange’s equation Lagrangian dynamics linear matrix elements obtain one-dimensional parameter particle of mass perturbation theory potential energy probability Problems in Classical Publishing AG 2017 quadratic Quantum Mechanics quantum number radius region result rmin shown in Fig simple harmonic motion sinÂ ſº Solution solve sphere spherical harmonics spin Springer International Publishing symmetric TISE total energy Ueff uncoupled unitless unperturbed vanishes vector velocity wave function zero