## Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and ResearchersA series of seminal technological revolutions has led to a new generation of electronic devices miniaturized to such tiny scales where the strange laws of quantum physics come into play. There is no doubt that, unlike scientists and engineers of the past, technology leaders of the future will have to rely on quantum mechanics in their everyday work. This makes teaching and learning the subject of paramount importance for further progress. Mastering quantum physics is a very non-trivial task and its deep understanding can only be achieved through working out real-life problems and examples. It is notoriously difficult to come up with new quantum-mechanical problems that would be solvable with a pencil and paper, and within a finite amount of time. This book remarkably presents some 700+ original problems in quantum mechanics together with detailed solutions covering nearly 1000 pages on all aspects of quantum science. The material is largely new to the English-speaking audience. The problems have been collected over about 60 years, first by the lead author, the late Prof. Victor Galitski, Sr. Over the years, new problems were added and the material polished by Prof. Boris Karnakov. Finally, Prof. Victor Galitski, Jr., has extended the material with new problems particularly relevant to modern science. |

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### Contents

1 Operators in quantum mechanics | 1 |

2 Onedimensional motion | 32 |

3 Orbital angular momentum | 84 |

4 Motion in a sphericallysymmetric potential | 116 |

5 Spin | 165 |

6 Timedependent quantum mechanics | 213 |

7 Motion in a magnetic field | 270 |

8 Perturbation theory Variational method Sudden and adiabatic theory | 296 |

10 Identical particles Second quantization | 447 |

11 Atoms and molecules | 485 |

12 Atomic nucleus | 598 |

13 Particle collisions | 637 |

14 Quantum radiation theory | 776 |

15 Relativistic wave equations | 810 |

16 Appendix | 866 |

871 | |

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according to Eq angles antiparticle asymptotic Born approximation bound calculate charge classical coefﬁcient coincides commutation compare to Problem Compare with Problem considered coordinate corresponding deﬁned deﬁnite value dependence described determined dipole Dirac equation eigenfunctions eigenvalues electric ﬁeld electron energy levels energy spectrum equal exact expression fermions ﬁnal ﬁnd ﬁnite ﬁrst order Green function Hamiltonian Hence Hermitian Hermitian operator hydrogen atom inﬁnite integral interaction isospin large distances level shift magnetic ﬁeld magnetic moment matrix element mean value momenta motion muon normalized nuclear nucleon nucleus obtain operator optical theorem oscillator parameter parity perturbation theory photon polarization previous problem probability quantum numbers quasi-classical radius reﬂection relation result of Problem rotational satisﬁes scattering amplitude scattering cross-section scattering length Schrodinger equation Solution speciﬁc spherical spinless particle spinor stationary symmetry takes the form Taking into account term transformation transition unperturbed vector wavefunction zero