Theoretical physics with sympy
summary
Introduces SymPy basics and then applies them to a concrete Heisenberg-style model of 2D layered magnets, deriving symbolic expressions, simplifying with CSE, solving for the phase angle and producing a numerical estimate of a transition point (analytic checks like 1/6 appear), converting to fast functions with lambdify + numpy vectorize, scanning parameter space to build phase diagrams and psychedelic-looking figures, and notes that heavy simplifications can take minutes but the workflow from symbolics to numeric plots works end to end.
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chapters (15)
- 0:00Introduction
- 3:08variables
- 6:26functions
- 8:45solving equations
- 11:55CSE
- 13:00Substitution
- 15:25Linear algebra
- 17:00Magnetism
- 19:05Heisenberg model
- 19:58Spiral unser
- 21:38Image sets
- 22:32Numerical solutions
- 23:27Combining solutions
- 27:33Syntax tree
- 29:42Plots
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