Welcome to the coming up to speed summer course 2025!
The idea of the course is to give an intuitive foundation to some important concepts in math, coding, classical mechanics, and quantum mechanics at the undergraduate physics level. The target audience is graduate students that are about to start their PhDs, but everyone at any career stage is welcomed if this would be useful for them.
Super important, during the lectures, while using the forum, and basically always in life: be nice to others and yourself. We abide by good rules on how to do that, I borrow in particular these two code of conducts: FRIB Code of Conduct | Facility for Rare Isotope Beams and Physics and Astronomy MSU code of conduct.
Github repository with useful things: GitHub - ascsn/online-guides: Compilation of the online guides for the incoming grad students
Youtube channel where the lectures are recorded. For example, last year’s the first lecture
Google drive with materials from last year’s lectures.
We will meet twice a week. The menu for this year will be very similar to last year’s, with ~ 2 weeks fully dedicated to math+coding, and the next 6-8 weeks alternating between classical (Mondays) and quantum mechanics (Wednesdays).
Mathematical and coding background: 2 weeks
- Derivatives and Integrals
- Taylor Series
- Vector calculus
- Differential equations
- Linear algebra
- Vectors and matrices
- Projections
- Change of basis
- Eigensystems
- Complex numbers
- Fourier transforms
- Basic python (operations, lists, plotting)
- Use of codespaces, AI, and documentations to get started
Classical Mechanics: 6-8 weeks
- Newtonian approach
- Constraining things (by deduction - arc length, etc. - and Lagrange multipliers)
- Moving things
- Rotating things
- Central forces and Orbits
- Normal modes and waves
- Lagrangian and Hamiltonian mechanics
Quantum Mechanics: 6-8 weeks
- Representations
- “Everything is linear algebra”
- Dirac’s notation
- Schrodinger equation
- Eigenstates → “Normal modes”
- Evolution operator
- Bound states and scattering states
- The Harmonic Oscillator
- Creation and annihilation operators
- Angular momentum, spins, groups, and all that
- Scattering theory
- Perturbation theory