Course title
02128700
Fundamentals of relativity and quantum mechanics

 takagahara toshihide

nakamura tota Click to show questionnaire result at 2017
Course description
Relativity and quantum mechanics are most important subjects in modern physics. In this course, we explain the fundamentals of special relativity and quantum mechanics. In the first part, we introduce the notion of length contraction, time dilation by using the Lorentz transformation. We also explain relativistic motions and the equivalence of mass and energy. In the second part, we introduce wave-behavior of quantum scale objects and explore the general aspect of the Schrodinger equation. Furthermore, we solve the equation as an eigenvalue problem in one-dimensional case. We also give an outline of the structure of hydrogen atom.
Purpose of class
This class is prepared for understanding the fundamentals of relativity and quantum mechanics, which are widely applied to modern technology such as a semiconductor or GPS devices
Goals and objectives
  1. Students should be able to explain the relativistic principle and show invariance of the speed of light by using Lorentz transformation.
  2. Students should be able to understand the relativistic equation of motion for a particle associated with four velocity and momentum. It is also required to understand the Newtonian mechanics as a non-relativistic limit of the equation.
  3. Students should be able to explain wave-particle duality and the Compton effect.
  4. Students should be able to calculate expectation values of mechanical variables and understand the nature of eigen values/functions.
  5. Students should be able to write Schrodinger equation and solve it in one-dimensional simple case such as square-well potential.
  6. Students should be able to solve one-dimensional scattering problems by the Schrodinger equation.
Language
English
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. The brief history of light investigation, Michelson-Morley experiment, and Galilei transformation two-dimensional matrix calculation, see page 70 in reference 1 190minutes
2. Galilei transformation and Lorentz transformation, time dilation, length contraction See pages 76, 90 with respect to Lorentz trans. in reference 1 190minutes
3. Four-velocity, peculiar time, twin paradox See Sec. 6 with respect to peculiar time, four-velocity in reference 1 190minutes
4. Four-momentum, relativistic mass, relativistic motion See Sec. 6.2 with respect to momentum, relativistic motion 190minutes
5. The application of special relativity: Doppler effect of light See Sec. 6.6 with respect to mass and energy in reference 1 190minutes
6. Introduction of Old quantum theory: hypothesis of light quanta, de Broglie wave, Euler’s formula See Sec. 2.3, 3.2 in reference 2 190minutes
7. Introduction of Wave mechanics: Plane wave equation,
Vector Analysis 		See Sec. 3.2, 3.3 in reference 2 190minutes
8. Wave mechanics I: operators in Quantum Mechanics, EV, Schrodinger equation and conservation law See Sec. 3 in reference 2 190minutes
9. Wave mechanics II: separation of variables, eigenvalue problem, Ehrenfest theorem See Sec. 3 in reference 2 190minutes
10. One-dimensional Schrodinger equation I: square well problems. See Sec. 6 in reference 2 190minutes
11. One-dimensional Schrodinger equation II: scattering problems See Sec. 7 in reference 2 190minutes
12. The outline of Schrodinger equation on central force field See Sec. 10 in reference 2 190minutes
13. Overall review See the whole part of references 1 and 2 190minutes
14. Terminal examination and final comments Review of the whole part of references 1 and 2 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 terminal exam. and reports Total.
1. 16% 16%
2. 17% 17%
3. 16% 16%
4. 17% 17%
5. 17% 17%
6. 17% 17%
Total. 100% -
Evaluation method and criteria
Exams 70% Mark participation 30%, acquisition of credits for 60%
Textbooks and reference materials
K. Kobayashi, ``Special relativity based on analytic continuation", Kogakusha (reference 1)
T. Sugiyama, ``Quantum mechanics I" Kodansha (reference 2)
Prerequisites
It is required to have a knowledge of fundamentals of mathematics and classical mechanics. It is preferred that you have already earned or are expected to earn in the same semester the credits of "Electricity and Magnetism" and "Thermal and Statistical Mechanics."
Office hours and How to contact professors for questions
  • Friday 12pm-14pm (It's advisable to make a reservation beforehand)
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
Active-learning course
About half of the classes are interactive
Last modified : Wed Oct 17 06:19:41 JST 2018