INTRODUCTION TO QUANTUM MECHANICS

理工学部 - 理工学部共通科目(英語コース)

SCT6760E

コース情報

担当教員: 井村 健一郎

単位数: 2

年度: 2024

学期: 秋学期

曜限: 水5

形式: 対面授業

レベル: 200

アクティブラーニング: なし

他学部履修: 不可

評価方法

授業参加

50%

その他

presentation

50%

詳細情報

概要

Quantum mechanics is the fundamental theory of atoms, molecules, elementary particles, or matter in general, and even that of information. This course is intended to be a “modern” introduction to such quantum mechanics of matter and information. Traditionally, quantum mechanics is described by the wave function, “psi,” which obeys the Schroedinger equation, while an alternative description based on the density matrix is also possible, which is often employed in the field of quantum information. Here, we attempt to make a bridge between these two complementary descriptions of the quantum mechanics. The first part of the course is mainly devoted to introduction of the basic concepts, while in the second part, we will apply them to some concrete problems such as potential problems of the Schroedinger equation as well as to problems related to the concept of quantum entanglement.

目標

Understanding of the basic notions of quantum mechanics and acquisition of practical techniques for applying it to some simple concrete problems.

授業外の学習

Reading of a relevant literature (e.g., a chapter of a textbook suggested in the lecture) and attempt to solve some homework exercises for digesting the content of the lecture

所要時間: 190 mins

スケジュール

  1. Road to quantum mechanics: Bohr’s model, de Blogile wave length, etc.
  2. The Schroedinger equation, Hamiltonian and its eigenenergy (spectrum), momentum in quantum mechanics
  3. What is a quantum state? and/or interpretation of quantum mechanics: wave function, probability amplitude
  4. Principles of quantum mechanics: superposition, Hilbert space, Hermitian operators
  5. Representations and notations of quantum mechanics: Fourier transform, Dirac’s brackets, commutator, and the uncertainty principle
  6. Two-level systems, Pauli matrices, and the density matrix
  7. D potential problems: bound vs. scattering states, discrete vs. continuous energy spectrum
  8. Analytic vs. numerical solutions, continuous vs. lattice models
  9. Harmonic oscillator: creation and annihilation operators, zero-point energy
  10. Angular momentum and its quantization, role of rotational symmetry, symmetry vs. conservation law
  11. Spin 1/2 and addition of spins: spin singlet vs. triplets, entangled spins
  12. Quantum mechanics of information
  13. Notion of the entanglement entropy, and so forth...
  14. Quantum mechanics of matter vs. quantum mechanics of information

教科書

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    参考書

    • Introduction to Quantum Mechanics (3rd edition)

      著者: Griffiths, David J.

      出版社: Cambridge University Press, 2018

    • Quantum Mechanics: Fundamentals (2nd edition)

      著者: Kurt Gottfried, Tung-Mow Yan

      出版社: Springer

    • Modern Quantum Mechanics

      著者: J. J. Sakurai, Jim Napolitano

      出版社: Cambridge University Press

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