Physical Math Course
Dive into Physical Mathematics Essentials Course to gain mastery over Gaussian integrals, ladder operators, and perturbation theory. Develop strong intuition for Schrödinger equations and quantum oscillator systems, empowering you to tackle real-world quantum challenges using precise and reliable mathematical methods with full confidence.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
This course equips you with practical techniques for Gaussian integrals, analytic continuation, and ladder operator algebra. Learners handle dimensionless Schrödinger equations, normal ordering of x⁴ terms, and non-degenerate perturbation theory, while evaluating series expansions and asymptotic behaviour to determine reliability of first-order corrections in practical computations.
Elevify advantages
Develop skills
- Master Gaussian integrals for computing oscillator norms using complex parameters.
- Utilise ladder operators to construct eigenstates and compute x, p, and number operators.
- Normal-order x⁴ expressions to simplify vacuum and excited-state expectation values.
- Apply perturbation theory to derive first-order energy shifts in anharmonic oscillators.
- Rescale Schrödinger equations into dimensionless forms for numerical stability.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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