Lecture Notes: Introduction to Quantum Mechanics (Course 804, Spring 2013)

Course Introduction

• Instructor: Allan Adams, Assistant Professor in Course 8
• Focus Areas: String theory, gravity, quantum gravity, condensed matter physics
• Recitation Instructors: Barton Zwiebach, Matt Evans (new faculty), TA: Paolo Glorioso

Course Logistics

• Website: All course materials on Stellar (lecture notes, homeworks, exams, grades)
• Videotaping: Lectures will be recorded for MIT OpenCourseWare; students can choose seating to avoid being filmed

Course Goals

• Objective: Learn quantum mechanics beyond calculations; develop intuition for quantum phenomena
• Effort Required: Concerted effort needed to develop intuition through problem-solving
• Problem Sets:
  • Due Tuesdays by 11 AM (sharp) in the physics box
  • Lowest problem set score will be dropped
  • Encourage collaboration, but write up solutions independently

Assessment Structure

• Exams: Two midterms and one final exam
• Clickers: Required for participation and non-graded quizzes; will contribute marginally to overall grade

Textbook Recommendations

• No specific textbook chosen; several recommended texts covering different aspects of quantum mechanics (wave mechanics and matrix mechanics)
• Weekly readings from recommended texts provided along with problem sets
• Collaboration encouraged to cover diverse textbooks without needing to purchase all

Class Participation

• Questions are encouraged during lectures; don't hesitate to interrupt
• Office hours available for further clarification on topics

Lecture Content Overview

First Lecture: Experiments with Electrons

• Discussion: Introduced concepts of color and hardness of electrons (not technical names)
  • All electrons observed are either black or white (binary property)
  • Hardness is either hard or soft (also binary)
• Color and Hardness Boxes: Devices that measure these properties with specific outputs
  • Color box: white aperture for white electrons, black aperture for black electrons
  • Hardness box: soft aperture for soft electrons, hard aperture for hard electrons

Key Experimental Findings

• Repeated measurements of color or hardness yield consistent results (e.g., a white electron remains white when re-measured)
• Independence of Properties: Measuring color does not predict hardness (50-50 distribution)
• Correlations: Properties appear uncorrelated; knowing one provides no information about the other

Surprise Experiments

• Conducted various thought experiments leading to contradictions in logic:
  • Inserting barriers into paths of electrons changes outcomes, affecting predictability of results
  • Essential conclusion: Cannot build a reliable box to simultaneously measure both properties of an electron
• Uncertainty Principle: Not just about measurement but intrinsic properties of particles
  • Presence of properties like color and hardness creates a superposition state where both cannot be defined at once

Concept of Superposition

• What is Superposition?: New fundamental idea in quantum mechanics where particles can exist in multiple states simultaneously
• Understanding Superposition: Requires a new language of quantum mechanics; traditional intuition is inadequate for quantum behaviors
• Examples illustrate that particles like electrons do not behave in predictable ways under classical logic

Looking Forward

• Aim of the course is to develop a new intuition for quantum mechanics and superposition concepts
• Next class will build upon this foundational understanding

Final Thoughts

• Engagement Encouraged: Questions and curiosity will help deepen understanding of challenging concepts throughout the course.