Quantum Mechanics Lecture Notes (MIT 804, Spring 3/21/2013)

Instructor Introduction

• Lecturer: Allan Adams, Assistant Professor in Course 8 (Physics)
• Specialization: String theory, gravity, quantum gravity, and condensed matter physics
• Team: Barton Zwiebach, Matt Evans (recitation instructors), Paolo Glorioso (TA)

Course Logistics

• Platform: Stellar website (lecture notes, homeworks, exams, grades)
• Recording: Lectures are videotaped for MIT OCW
• Materials: Four recommended textbooks covering wave mechanics (PDE) and matrix mechanics (linear algebra)

Course Goals and Workload

• Develop intuition in quantum mechanics beyond just calculations
• Importance of solving problems for developing intuition
• Assignments: Weekly problem sets due every Tuesday by 11 AM, no late submissions but lowest score is dropped
• Exams: Two midterms and one final exam
• Tools: Clickers required for participation, contribute to overall grade

Key Concepts in Quantum Mechanics

Introduction to Quantum Mechanics

• Quantum mechanics is not fundamentally hard but requires effort and problem-solving
• Goal: Develop intuition for quantum phenomena

Fundamental Experiments with Electrons

Electron Properties

• Color: Electrons are either black or white
• Hardness: Electrons are either hard or soft
• Devices: Color box and hardness box to measure these properties

Experiments and Observations

• Repeatability: Measurements are consistent on repeated trials
• Color box repeatedly measures the same color (black or white)
• Hardness box repeatedly measures the same hardness (hard or soft)

Independence of Properties

• Measuring one property (color) gives no information about the other (hardness), and vice-versa
• Examples:
  • White electrons show 50% hard and 50% soft when passed through a hardness box
  • Soft electrons show 50% black and 50% white when passed through a color box

Surprising Results

• Introducing a hardness box between two color boxes disrupts initial color measurement
• Electrons do not persistently stay black or white after passing through a hardness box
• Properties appear to be influenced/changed by measurement

Conceptual Challenges and Conclusions

Probabilistic Nature

• Measurements in quantum mechanics are fundamentally probabilistic
• Probability in quantum mechanics is not due to experimental limitations

Uncertainty Principle

• Uncertainty Principle: Certain properties (color and hardness) cannot be simultaneously known/measured
• Implications: Impossible to construct a reliable device measuring both color and hardness simultaneously

Concept of Superposition

• Electrons exist in a state of superposition: they are not strictly hard or soft, black or white
• Experimental Validation: Various setups confirm predictions about superposition states
  • Mirroring setup experiments leading to intriguing results, such as never seeing split or indefinite electrons
• Conclusion: Classical determinism does not apply; quantum mechanics operates in a fundamentally different and non-intuitive manner

Intuition Development

• Developing an intuition for quantum mechanics requires understanding and accepting superposition and probabilistic nature
• Quantum mechanics contradicts classical expectations developed from everyday experiences

Final Remarks

• The behavior observed in electrons applies universally to atoms, molecules, and larger systems under specific conditions
• Learning quantum mechanics involves adjusting to an entirely new framework of understanding the physical world

Homework: Engage with problem sets actively to develop intuition and understand fundamental quantum mechanical phenomena