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Schedule for INSIGHT Physics Immersion Week (June 21 - June 25)

Monday June 21, 10am-1pm EDT/7am-10am PDT (Instructor: Julie)

Relevant Topics to Review Before Class

  • Classical Two-Body Problem
  • Basic Python programming including the NumPy and Matplotlib libraries
  • The Velocity-Verlet Method

Class Schedule (10am-12pm EDT, 12pm EDT is set aside as an extra office hour)

  • 10:00-10:30: Introduction to the course and Q&A on the pre-course assignments (additional questions can be asked during the office hour immediately after class)
  • 10:30-11:00: Lecture on the classical two-body problem and how to translate a two-body problem to Python code. View the lecture notes here and the hand-written notes here.
  • 11:00-12:00: Group Learning Activity - In groups of approximately 4 create a Python code that models the Earth-Sun two-body system. Once correct, try to extend the problem to model two electrons, and finally two atoms. A more detailed problem statement can be found here. Questions can be asked about the project during class and after class during the office hour.

Learning Goals for Day

  • Students should understand the concepts behind the classical two-body problem and be able to write down the equations that are used to solve it.
  • Students should demonstrate how the Velocity-Verlet method can be used to computationally model the motion of an object given a force.
  • Students should create a Python program that models the earth-sun system and compare it to the expected, analytical answer.
  • Students should be able to extend their two-body Python program to model two electrons and two nucleons.

Homework Assignment for Tuesday

  • Complete the coding assignment from day including the two bonus activites.
  • Challenge Problem: Extend one of the two-body problems discussed in class (Earth-Sun, two electrons, or two nucleons) to a three body problem (Earth-Sun-Moon, three electrons, or three nucleons). Verify through graphs the the programs gives the expected answers.
  • Read the this introduction to quantum mechanics from "No Nonsense Quantum Mechanics" and this introduction to linear algebra from Carnegie Mellon University
  • Review the lecture notes for Tuesday located here. (TO-DO: Add document)

Tuesday June 22, 10am-1pm EDT/7am-10am PDT (Instructor: Julie)

Relevant Topics to Review Before Class

  • Basics statistics such as averages and standard deviations
  • Derivatives and integrals in one or more variables
  • Complex numbers, complex conjugates, etc.

Class Schedule (10am-12pm EDT, 12pm EDT is set aside as an extra office hour)

  • 10:00-10:50: Lecture on the the breakdown of classical mechanics and the basics of quantum mechanics including an introduction to wave-particle duality and uncertainty and why we need probabilities in quantum mechanics. View the lecture notes here, the recording here, and the hand-written notes here.
  • 10:50-11:00: Break with time for questions
  • 11:00-11:50: Lecture on more quantum mechanics basics with an introduction to linear algebra and how quantum mechanics can be formulated as a linear algebra problem. View the lecture notes here, the recording here, and the hand-written notes here.
  • 11:50-12:00: Q&A session and homework help (Monday or Tuesday homework). Can be extended into the 12pm-1pm office hour time slot.
  • A series of short questions will be asked and discussed during the lectures to help you check your understanding of the material.

Learning Goals for Day

  • Students should be able to solve linear algebra problems involving multiplication, eigenvalues, and eigenvectors by hand.
  • Students should be able to explain why quantization and the uncertainity principle arrive from the wave-like nature of particles.
  • Students should be able to demonstrate the following properties of wavefunctions: superposition principle, normalization, and finding probabilities.
  • Students should be able to symbolically calcualte expectation values.

Homework Assignment for Wednesday

  • Complete this activity to review the quantum mechanics and linear algebra concepts learned today.
  • Review the lecture notes for Wednesday located here.

Wednesday June 23, 10am-1pm EDT/7am-10am PDT (Instructor: Morten)

  • 10:00-10:50: Lecture on eigenvalue problems and classical two-point boundary value problem. Example system: spring or beam fastened in both ends and quantization. View the lecture notes here, view the recording here, and the hand-written notes here.
  • 10:50-11:00: Break with time for questions
  • 11:00-11:50: More on two-point boundary value problems and how to solve eigenvalue problems with Numpy. Develop code for two-point boundary value problem and study analytical and numerical solutions. See the lectures for example code here, view the recording here, and the hand-written notes here.
  • 11:50-12:00: Q&A session and homework help (Wednesday's homework). Can be extended into the 12pm-1pm office hour time slot.
  • A series of short questions will be asked and discussed during the lectures to help you check your understanding of the material.

Learning Goals for Day

  • Students should understand how to discretize a differential equation and scale the equations.
  • Students should understand how a two-point boundary value problem from a second-order differential equation can be changed into an eigenvalue problem.
  • Students should create a Python program that solves a two-point boundary value for a spring/beam fastened at both ends.
  • Students should be able to compare the numerical eigenpairs (eigenvalues and eigenvectors) with the given analytical ones.

Homework Assignment for Thursday

Thursday June 24, 10am-1pm EDT/7am-10am PDT (Instructor: Morten)

  • 10:00-10:50: Lecture on eigenvalue problems and quantum mechanical two-point boundary value problem. Example system: particle in a box potential or similar one-particle problems. View the lecture notes here, view the hand-written notes here.
  • 10:50-11:00: Break with time for questions
  • 11:00-11:50: How to solve quantum mechanical eigenvalue problem for particle confined to move in a potential. Develop code for two-point boundary value problem and study analytical and numerical solutions. See the lectures for example code here. We will reuse the code from Wednesday. The only addition which is needed is the given potential. See the recording here.
  • 11:50-12:00: Q&A session and homework help (Thursday's homework). Can be extended into the 12pm-1pm office hour time slot.
  • A series of short questions will be asked and discussed during the lectures to help you check your understanding of the material.

Learning Goals for Day

  • Students should understand how a one-particle problem can be rewritten as a two-point boundary value problem.
  • Students should understand the difference between bound and unbound states.
  • Students should create a Python program that solves the time-independent single-particle Schroedinger equation.
  • Students should be able to extend their code to other types of confining potentials/interactions.

Homework Assignment for Thursday

Friday June 25, 10am-1pm EDT/7am-10am PDT (Instructor: Linda, Julie, Morten)

Class Schedule

  • 10:00-10:30: Derivation of the harmonic oscillator starting from Hooke's law as well as an overview of Taylor expansions (Linda)
  • 10:30-10:40: Break with time for questions
  • 10:40-11:10: Introduction to the quantum harmonic oscillator and how it can be derived from the classical case. Conceptual introduction to ladder operators and harmonic oscillator states. (Julie)
  • 11:20-11:30: Break with time for questions
  • 11:30-12:00: Group Learning Activity - Create a Python program which models the motion of a particle under the influence of the classical harmonic oscillator (hint: think about the eigenvalue method we have studied Wednesday and Thursday). We can in turn extend this to two interacting particles using the separation of variables into relative and center-of-mass coordinates (Morten)