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MIT Quantum Mechanics Lecture Notes

Jul 27, 2024

Notes from MIT Introduction to Quantum Mechanics Lecture 1

Introduction

  • Instructor: Allan Adams
  • Spring 2013, Course 804 (Quantum Mechanics)
  • Background: Studying string theory, gravity, quantum gravity, and condensed matter physics.
  • Course Objective: Learn quantum mechanics, focusing on developing intuition rather than just calculations.

Course Structure

  • Instructors:
    • Recitation: Barton Zwiebach (experienced) and Matt Evans (new).
  • Teaching Assistant: Paolo Glorioso.
  • Course Materials: Everything will be available on the Stellar website - including notes, homework, exams, and grades.
  • Video Recording: Classes will be videotaped; students who prefer not to be recorded should sit at the sides.

Work Expectation and Policies

  • Problem Sets:
    • Due Tuesday by 11 AM in the physics box.
    • Late work not accepted, but the lowest score will be dropped.
    • Collaboration encouraged, but students must write up their own solutions.
  • Exams:
    • Two midterms, date to be announced.
    • One final exam.
  • Clickers will be used for participation questions and will contribute to the overall grade.
    • Students should register their clickers by next week.

Recommended Textbooks

  • No single required textbook; a list of recommended texts will be provided to cover different approaches (wave mechanics vs. matrix mechanics).

Class Culture

  • Students are encouraged to ask questions at any time during lectures or recitation sessions to ensure comprehension.
  • Questions from Students:
    • No late submissions allowed unless discussed ahead of time.
    • Videos of lectures will be available later on the OCW website.

Lecture Content: Introduction to Quantum Mechanics

Philosophical Foundation

  • Discussing foundational ideas from David Albert's book: Quantum Mechanics and Experience.
  • Focus on peculiar properties of electrons:
    • Mysterious experiments involving color and hardness (2 binary properties).

Experimental Setup

  • Color Box: Measures whether electrons are black or white.
  • Hardness Box: Measures whether electrons are hard or soft.
  • Both properties must be measured independently, indicating they are uncorrelated.

Key Experiment: Color and Hardness Correlation

  1. Send a set of electrons through a color box.
  2. Measure outcomes of color and hardness using boxes.
  3. Findings show no correlation: knowing one does not give information about the other.
  4. Persistently measured properties reveal unpredictability and randomness of electron behavior, challenging traditional views.
    • If you measure the color, the hardness cannot be predicted.

Superposition Concept

  • Big Idea: Many outcomes cannot be attributed to specific paths or properties of electrons as they behave in ways unlike macroscopic objects.
  • Superposition: Electrons exist in a state where they can represent multiple outcomes simultaneously until measured.
  • Breaking down intuition developed from classical physics to embrace quantum mechanics.
    • Challenge: Develop a new intuition about quantum behavior over the course.

Conclusions on Nature of Electrons

  • Experiments lead to the conclusion that electrons are neither one path nor another but exist in a superposed state.
  • Fundamental properties of particles cannot be described in classical terms and require quantum language.

Summary of Key Concepts

  • Definitional Properties of Electrons: Color and hardness as non-correlated properties.
  • Experimental Observations: Challenge understanding of how particles behave; lead to the development of quantum mechanics concepts such as superposition.
  • Intuition Shift: Move from classical to quantum thinking for further understanding in the course.