Quantum Mechanics (Lecture by Allan Adams)

Instructor and Course Info

• Instructor: Allan Adams
• Course: 804, Spring 2013
• Specializations: String theory, gravity, quantum gravity, condensed matter physics
• Teaching a course on: Quantum Mechanics
• Assistants: Barton Zwiebach, Matt Evans (new faculty), Paolo Glorioso (TA)

Administrative Details

1. Website: Stellar (Lecture notes, homeworks, exams, and grades)
2. Videotaping for OCW: Avoid camera by sitting on the sides
3. Objective: Develop intuition for quantum phenomena, not just calculations
4. Problem Sets: Recommendations
   • Work hard and collaborate on problem sets
   • Problem sets due every Tuesday at 11 AM
   • No late work accepted; lowest problem set score will be dropped
5. Exams:
   • Two midterms, dates TBD
   • One final exam
6. Clickers:
   • Required for participation and concept questions
   • Contribute to overall grade
7. Textbooks: No specific textbook, four recommended, variety of additional references
8. Asking Questions: Encouraged in lectures, office hours, and recitations

Syllabus Overview & Expectations

• Effort Required: Quantum mechanics is challenging but manageable
• Intuition Development: Solving problems is essential

Quantum Mechanics: Key Concepts/Experiments

Properties of Electrons

• Characteristics: Color and Hardness
  • Color: Either black or white (binary)
  • Hardness: Either hard or soft (binary)

Measurement Devices

• Color Box: Determines an electron's color (Black/White)
• Hardness Box: Determines an electron's hardness (Hard/Soft)
• Consistency: Repeated measurements on the same electron yield the same results

Correlation Between Properties

• Color and Hardness Independence:
  • Measuring color does not predict hardness and vice versa.
  • Example: Sending a white electron through a hardness box results in a 50/50 hardness distribution

Experiment Setup

• Basic Experimental Design:
  • Set up a series of measurements (color and hardness)

Key Experiments

1. Experiment 1: Sending white electrons into a hardness box

   • Prediction: 50% hard, 50% soft
   • Results: Mirrors do not change electron properties

2. Experiment 2: Sending hard electrons into a color box

   • Prediction: 50% black, 50% white

3. Experiment 3: Initial white electrons into a hardness box, measuring color

   • Prediction: Output as 50-50
   • Unexpected Result: 100% white electrons

Advanced Experiments

1. Experiment 4: With a barrier in the soft path
   • Results: Down by 50%, but 50% white, not 100%

Conceptual Understanding and Implications

• Superposition and Uncertainty Principle:
  • Electrons may not take a definitive path (hard/soft or both/neither)
  • Experiments challenge classical determinism
• Empirical Lessons:
  • Experiment results are consistent regardless of the materials or setup

Experimental Puzzles & Thought Exercises

• Reflection on Path of Electrons:
  • Can’t infer traditional paths or states – introduces the need for new terminologies
  • Superposition: New way to describe electron behavior

Conclusion

• Quantum mechanics challenges classical intuition but aligns with empirical observations
• Goal: Develop a new intuition aligned with quantum principles