Introduction to Special Relativity and Quantum Mechanics

Curriculum Guideline

Effective Date:
Course
Discontinued
No
Course Code
PHYS 2250
Descriptive
Introduction to Special Relativity and Quantum Mechanics
Department
Physics
Faculty
Science & Technology
Credits
3.00
Start Date
End Term
Not Specified
PLAR
No
Semester Length
15 weeks
Max Class Size
36
Contact Hours

4 hours per week.   Some assignments might be online. 

Method(s) Of Instruction
Lecture
Learning Activities

Lectures

May include some online assignments.

Course Description
This course is an introduction to modern physics. The first part will focus on special relativity: Lorentz transformation, relativistic kinematics and dynamics, and conservation laws. The second part will focus on quantum mechanics: matter waves, early quantum models as well as the experimental evidence for quantization, a qualitative discussion of the concepts of quantum mechanics and their application to simple systems.
Course Content

Special Relativity

  • Galilean relativity
  • Events, measurements and simultaneity
  • Consequences of Special Relativity
  • Spacetime diagrams and paradoxes
  • Relativistic dynamics
  • Massless particles

Quantum Mechanics

  • Quantization of charge and light energy
  • Atomic spectra and the nuclear atom 
  • Wave packets and wave functions
  • Heisenberg Uncertainty Principle
  • The Schrödinger Equation
  • Applications of the Schrödinger Equation in one-dimension
  • Tunnelling and reflections
  • Hydrogen atom
  • Applications of Quantum Mechanics
Learning Outcomes

Upon successful completion of this course, students will be able to:

Special Relativity

  • explain what is meant by the principle of relativity, and give examples that appear to contradict this principle
  • describe how Einstein's postulates of Special Relativity lead to the relativity of simultaneity
  • transform spacetime coordinates and velocities between inertial reference frames using Lorentz transformations and velocity transformation
  • describe and calculate the relativistic effects of time dilation, length contraction, and the relativistic Doppler effect
  • use spacetime diagrams to graphically represent processes involving relativistic velocities
  • resolve common paradoxes such as "the twins paradox" and the "pole in the barn" paradox 
  • analyze dynamical processes using relativistic dynamics including particle decay and collisions
  • explain the relations between mass, energy and momentum in relativity and describe the consequences of these relations to massless particles

 Quantum Mechanics

  • explain the experimental evidence for the quantization of charge and light energy
  • give qualitative predictions and explanations of the behaviour of simple quantum systems, such as the distribution of electrons in atoms and the spectrum of light emitted and absorbed by atoms
  • explain the probabilistic interpretation of the wave function, and use the wave function to determine the expectated value of a measurement and the probability of various outcomes in simple quantum systems  
  • explain how a wave packet can be generated using a quantum superposition of eigenstates and apply the Heisenberg Uncertainty Principle to determine the time evolution of a wave packet
  • state the Schrödinger equation and the time-independent Schrödinger equation and explain how these equations govern the time evolution of wave functions
  • verify solutions of the Schrödinger equation for a free particle and 1D potentials such as the infinite square well, the finite square well, the step potential and finite barrier (tunnelling) 
  • qualitatively describe solutions to the 3D Schrödinger equation for the hydrogen atom (Coulomb potential), and the quantization of angular momentum

General

  • demonstrate an understanding of popular science articles on current research in physics by the ability to answer questions about modern physics from curious friends and relatives
  • value gaining a deeper understanding and appreciation of quantum mechanics and special relativity
Means of Assessment

Evaluation will be carried out in accordance with Douglas College policy. The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester. Evaluation will be based on the following:

In class and online assignments  10-30%

Tests (minimum of two during the semester)  30-50%

Final exam  30-40%

Textbook Materials

Consult the Douglas College Bookstore for the latest required textbooks and materials. An example textbook is Modern Physics by Paul Tippler and Ralph Llewellyn.

Prerequisites

PHYS 1110, PHYS 1210, and MATH 1220 

Recommended prerequisites: MATH 2232 Linear Algebra and MATH 2321 Calculus III. 

 

Corequisites

Recommended co-requisite: MATH 2421 Ordinary Differential Equations.

Which Prerequisite

None.