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PHY309

Quantum Mechanics I

  • Sciences
  • 300 level
  • 3 credit units
  • 153 pages
  • 9 units

This course, Quantum Mechanics I, introduces the fundamental principles governing the behavior of matter at the atomic and subatomic levels. It begins with a review of essential mathematical concepts, including vector spaces and operators. The course explores the inadequacies of classical mechanics, leading to the introduction of the Schroedinger equation and postulates of quantum mechanics. Students will learn to solve time-independent Schroedinger equations for various potentials, including infinite and finite potential wells, and the harmonic oscillator.

About this course

Difficulty
Intermediate
Study hours
150 hours
Maths
Advanced
Content
Theoretical, problem solving
Practical work
No
Before you start
  • Calculus
  • Linear Algebra
  • Classical Mechanics
  • Electromagnetism
How it is assessed
  • Tutor Marked Assignments
  • End of Course Examination

One paragraph, so you can see how it reads

PHY309 · Unit 2: Orthogonality and Orthonomality

Example 3: The space of square integrable complex valued functions, s F , over the interval ] , [ b a , i.e., s F x f  ) ( implies that    b a dx x f 2 ) ( .

What you should be able to do

  1. Understand the mathematical foundations of quantum mechanics.
  2. Identify the limitations of classical mechanics.
  3. Apply the Schroedinger equation to solve quantum mechanical problems.
  4. Interpret the solutions of the Schroedinger equation.
  5. Calculate probabilities and expectation values in quantum systems.
  6. Apply ladder operators to solve the harmonic oscillator problem.
  7. Explain the postulates of quantum mechanics.

What it prepares you for

Careers
  • Theoretical Physicist
  • Research Scientist
  • Quantum Computing
  • Materials Scientist
  • Data Scientist
Where it is applied
  • Quantum Computing
  • Materials Science
  • Electronics
  • Telecommunications
  • Nanotechnology
Tools
  • Mathematical software (e.g., Mathematica, MATLAB)

Where it gets hard

The units students slow down on, and what makes each one heavy.

  • Module 3: Time-Independent Schroedinger Equation in One Dimension I

    Unit 1: Bound States

    Requires strong understanding of differential equations and boundary conditions to solve for bound states.

  • Module 3: Time-Independent Schroedinger Equation in One Dimension I

    Unit 2: Scattering States

    Involves complex calculations of reflection and transmission coefficients, requiring careful attention to detail.

  • Module 4: Time-Independent Schroedinger Equation in One Dimension II

    Unit 1: The Simple Harmonic Oscillator

    Requires advanced mathematical techniques to solve the Schroedinger equation for the harmonic oscillator.

A suggested way through it

Suggested

13 weeks, about 42 hours in total. Yours will differ.

  1. Week 1Module 1: Vector Spaces and Operators
    • Unit 1: Vector Spaces · 3 hours

      Review the definition of vector spaces and their properties.. Practice identifying examples of vector spaces.. Solve problems involving linear independence and basis vectors..

  2. Week 2Module 1: Vector Spaces and Operators
    • Unit 2: Orthogonality and Orthonormality · 3 hours

      Study the concepts of orthogonality and orthonormality.. Learn to normalize vectors and functions.. Practice applying the Gram-Schmidt orthonormalization procedure..

  3. Week 3Module 1: Vector Spaces and Operators
    • Unit 3: Operators · 3 hours

      Understand the properties of linear operators.. Calculate eigenvalues and eigenvectors of linear operators.. Learn about expectation values and commutators..

  4. Week 4Module 2: Inadequacies of Classical Mechanics and the Schroedinger Equation
    • Unit 1: The Inadequacies of Classical Mechanics · 3 hours

      Identify the failures of classical mechanics in explaining certain phenomena.. Study blackbody radiation, photoelectric effect, and Compton effect.. Understand Bohr's theory of the hydrogen atom..

  5. Week 5Module 2: Inadequacies of Classical Mechanics and the Schroedinger Equation
    • Unit 2: The Schroedinger Equation · 3 hours

      Derive the time-dependent Schroedinger equation.. Deduce the time-independent Schroedinger equation.. Learn to interpret the Schroedinger equation and its solutions..

  6. Week 6Module 2: Inadequacies of Classical Mechanics and the Schroedinger Equation
    • Unit 3: Postulates of Quantum Mechanics · 3 hours

      Understand the postulates of quantum mechanics.. Learn to expand a wavefunction as a linear combination of eigenstates.. Calculate probabilities and expectation values..

  7. Week 7Module 3: Time-Independent Schroedinger Equation in One Dimension I
    • Unit 1: Bound States · 3 hours

      Define bound states and scattering states.. Solve the Schroedinger equation for a particle in an infinite potential well.. Apply boundary conditions to obtain the condition for bound states..

  8. Week 8Module 3: Time-Independent Schroedinger Equation in One Dimension I
    • Unit 2: Scattering States · 3 hours

      Study the potential step problem and calculate reflection and transmission coefficients.. Analyze the potential barrier problem and understand quantum tunneling.. Compare quantum mechanical results with classical predictions..

  9. Week 9Module 4: Time-Independent Schroedinger Equation in One Dimension II
    • Unit 1: The Simple Harmonic Oscillator · 3 hours

      Derive the Schroedinger equation for the harmonic oscillator.. Obtain the dimensionless form of the equation.. Solve the Schroedinger equation and find the allowed energy levels..

  10. Week 10Module 4: Time-Independent Schroedinger Equation in One Dimension II
    • Unit 2: Raising and Lowering Operators for the Harmonic Oscillator · 3 hours

      Learn about raising and lowering operators.. Understand the number operator and its properties.. Apply operator methods to solve the harmonic oscillator problem..

  11. Week 11Final Revision
    • Review of Modules 1-4 · 4 hours

      Review all modules and units.. Solve practice problems from each module.. Focus on key concepts and equations..

  12. Week 12Final Revision
    • Assignments and Revision · 4 hours

      Work on assignments and TMAs.. Consult with facilitator on difficult topics.. Prepare for the end-of-course examination..

  13. Week 13Final Revision
    • Final Revision · 4 hours

      Final revision and exam preparation.. Review key concepts and practice problems.. Focus on areas of weakness..

Preparing for the exam

What to do
  • Review all key definitions and theorems from each unit.
  • Practice solving a variety of problems from the textbook and TMAs.
  • Create concept maps linking mathematical methods to physical applications.
  • Focus on understanding the physical interpretations of mathematical solutions.
  • Prioritize time management during the exam by allocating time to each question.
  • Practice deriving key equations like Schroedinger's equation from first principles.
  • Review worked examples in the textbook to understand problem-solving strategies.
  • Create flashcards for important formulas and concepts for quick recall.
  • Attempt past exam papers to familiarize yourself with the exam format and difficulty level.

Questions students ask about this course

What is PHY309 about?

This course, Quantum Mechanics I, introduces the fundamental principles governing the behavior of matter at the atomic and subatomic levels. It begins with a review of essential mathematical concepts, including vector spaces and operators. The course explores the inadequacies of classical mechanics, leading to the introduction of the Schroedinger equation and postulates of quantum mechanics. Students will learn to solve time-independent Schroedinger equations for various potentials, including infinite and finite potential wells, and the harmonic oscillator.

How many units does PHY309 have?

PHY309, Quantum Mechanics I, has 9 units across 4 modules, over 153 pages of course material. You can read it one unit at a time.

How many credit units is PHY309?

PHY309 carries 3 credit units, at 300 level in Sciences.

Is PHY309 hard?

PHY309 is rated intermediate level, with advanced mathematical content. It is mostly theoretical and problem solving work.

How long does PHY309 take to study?

About 150 hours of study, spread across its 9 units.

How is PHY309 assessed?

PHY309 is assessed by Tutor Marked Assignments and End of Course Examination.

What do I need before starting PHY309?

Calculus Linear Algebra Classical Mechanics Electromagnetism

What can I do with PHY309?

Theoretical Physicist, Research Scientist, Quantum Computing, Materials Scientist and Data Scientist.

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