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PHY309Sciences3 Unitsintermediate

Quantum Mechanics I

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.

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150h
Study Time
13
Weeks
12h
Per Week
advanced
Math Level
Course Keywords
Quantum MechanicsSchroedinger EquationWave-Particle DualityOperatorsVector Spaces

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
Math Level
Advanced Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Vector Spaces and Operators

2

Inadequacies of Classical Mechanics

3

Schroedinger Equation

4

Postulates of Quantum Mechanics

5

Bound States

6

Scattering States

7

Harmonic Oscillator

8

Ladder Operators

Total Topics8 topics

Requirements

Knowledge and skills recommended for success

Calculus

Linear Algebra

Classical Mechanics

💡 Don't have all requirements? Don't worry! Many students successfully complete this course with basic preparation and dedication.

Assessment Methods

How your progress will be evaluated (2 methods)

Tutor Marked Assignments

Comprehensive evaluation of course material understanding

Written Assessment

End of Course Examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Theoretical Physicist

Apply your skills in this growing field

Research Scientist

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Quantum Computing

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Materials Scientist

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Data Scientist

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Industry Applications

Real-world sectors where you can apply your knowledge

Quantum ComputingMaterials ScienceElectronicsTelecommunicationsNanotechnology

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Vector Spaces and Operators

3h

Unit 1: Vector Spaces

3 study hours
  • Review the definition of vector spaces and their properties.
  • Practice identifying examples of vector spaces.
  • Solve problems involving linear independence and basis vectors.
Week
2

Module 1: Vector Spaces and Operators

3h

Unit 2: Orthogonality and Orthonormality

3 study hours
  • Study the concepts of orthogonality and orthonormality.
  • Learn to normalize vectors and functions.
  • Practice applying the Gram-Schmidt orthonormalization procedure.
Week
3

Module 1: Vector Spaces and Operators

3h

Unit 3: Operators

3 study hours
  • Understand the properties of linear operators.
  • Calculate eigenvalues and eigenvectors of linear operators.
  • Learn about expectation values and commutators.
Week
4

Module 2: Inadequacies of Classical Mechanics and the Schroedinger Equation

3h

Unit 1: The Inadequacies of Classical Mechanics

3 study 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.
Week
5

Module 2: Inadequacies of Classical Mechanics and the Schroedinger Equation

3h

Unit 2: The Schroedinger Equation

3 study hours
  • Derive the time-dependent Schroedinger equation.
  • Deduce the time-independent Schroedinger equation.
  • Learn to interpret the Schroedinger equation and its solutions.
Week
6

Module 2: Inadequacies of Classical Mechanics and the Schroedinger Equation

3h

Unit 3: Postulates of Quantum Mechanics

3 study hours
  • Understand the postulates of quantum mechanics.
  • Learn to expand a wavefunction as a linear combination of eigenstates.
  • Calculate probabilities and expectation values.
Week
7

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

3h

Unit 1: Bound States

3 study 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.
Week
8

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

3h

Unit 2: Scattering States

3 study 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.
Week
9

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

3h

Unit 1: The Simple Harmonic Oscillator

3 study 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.
Week
10

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

3h

Unit 2: Raising and Lowering Operators for the Harmonic Oscillator

3 study hours
  • Learn about raising and lowering operators.
  • Understand the number operator and its properties.
  • Apply operator methods to solve the harmonic oscillator problem.
Week
11

Final Revision

4h

Review of Modules 1-4

4 study hours
  • Review all modules and units.
  • Solve practice problems from each module.
  • Focus on key concepts and equations.
Week
12

Final Revision

4h

Assignments and Revision

4 study hours
  • Work on assignments and TMAs.
  • Consult with facilitator on difficult topics.
  • Prepare for the end-of-course examination.
Week
13

Final Revision

4h

Final Revision

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

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

Read the complete course material as provided by NOUN.

Access PDF Material

Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all key definitions and theorems from each unit.

2

Practice solving a variety of problems from the textbook and TMAs.

3

Create concept maps linking mathematical methods to physical applications.

4

Focus on understanding the physical interpretations of mathematical solutions.

5

Prioritize time management during the exam by allocating time to each question.

6

Practice deriving key equations like Schroedinger's equation from first principles.

7

Review worked examples in the textbook to understand problem-solving strategies.

8

Create flashcards for important formulas and concepts for quick recall.

9

Attempt past exam papers to familiarize yourself with the exam format and difficulty level.

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