Physical Math Course
Dive into this Physical Mathematics 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 solve real-world quantum challenges confidently using precise mathematical techniques and tools.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
This Physical Mathematics Course equips you with practical skills to tackle Gaussian integrals, analytic continuation, and ladder operator algebra. You'll handle dimensionless Schrödinger equations, normal ordering for x⁴ terms, and non-degenerate perturbation theory, while evaluating series expansions and asymptotic behaviour to determine reliable first-order corrections in practical computations.
Elevify advantages
Develop skills
- Master Gaussian integrals for computing oscillator norms with complex parameters.
- Harness ladder operators to construct eigenstates and compute x, p, and number operators.
- Normal-order x⁴ expressions to simplify vacuum and excited-state expectation values.
- Implement perturbation theory to derive first-order energy shifts in anharmonic oscillators.
- Rescale Schrödinger equations into dimensionless forms for stable numerical solutions.
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 workloadWhat our students say
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