Recommended exercises by school topic
This chapter contains lists of mathematics exercises grouped by each quantum chemistry topic taught at the school. These exercises can be useful as a warm-up to the proper exercises given each day.
The list is not complete, and is continually updated!
Coupled-cluster theory
Beginner
- Exercise 29.1 — Approximating the exponential function
- Exercise 30.1 — Exponential of a diagonal matrix
- Exercise 30.2 — An exponential whose series terminates
Intermediate
- Exercise 29.6 — From the exponential to rotations
- Exercise 30.4 — A matrix exponential and rotations
- Exercise 30.6 — A terminating similarity transformation
Second quantization
Beginner
- Exercise 3.1 — Very basic sums
- Exercise 3.2 — Simplifying as a sum
- Exercise 9.1 — Checking candidate eigenvectors
- Exercise 3.4 — Reconstruct a vector
- Exercise 3.6 — The summation index is a dummy index
- Exercise 3.7 — Linearity of sums
- Exercise 3.8 — When something does not depend on the summation index
- Exercise 3.9 — Free and summed indices
- Exercise 3.10 — Shifting the summation index
- Exercise 3.11 — The Kronecker delta: basic exercise
- Exercise 4.5 — Basic binomial coefficients
- Exercise 4.6 — Pascal’s triangle
- Exercise 4.9 — The binomial theorem
- Exercise 5.6 — Your first induction proof
- Exercise 22.1 — From components to a gradient
- Exercise 22.2 — Differentiating a quadratic form
Intermediate
- Exercise 9.3 — Eigenvalues and diagonalization of a Hermitian matrix
- Exercise 4.10 — Coefficients in binomial expansions
- Exercise 5.7 — Direct proof with a matrix
- Exercise 27.3 — The exponential, sine, and cosine series
- Exercise 27.7 — The Cauchy product of power series
For the curious
- Exercise 4.7 — Pascal’s identity
Self-consistent field theory
No exercises selected.
Density functional theory
No exercises selected.
Response theory
Beginner
- Exercise 22.4 — Treating \(c\) and \(c^*\) as independent variables
- Exercise 30.1 — Exponential of a diagonal matrix
- Exercise 30.2 — An exponential whose series terminates
Intermediate
- Exercise 30.4 — A matrix exponential and rotations
- Exercise 30.5 — Anti-Hermitian matrices and unitary matrices
- Exercise 30.6 — A terminating similarity transformation
Relativistic quantum chemistry
Beginner
- Exercise 3.12 — The Levi–Civita symbol: basic exercise
- Exercise 17.2 — Roots of a cubic polynomial by guessing and polynomial long division
Molecular properties
Intermediate
- Exercise 7.1 — The vector triple product and the Levi-Civita symbol
Multiconfigurational methods
No exercises selected.