Physical Math Course
Dive into advanced physical mathematics with this course, mastering Gaussian integrals, ladder operators, perturbation theory, and Schrödinger equations for oscillators. Gain confidence in tackling quantum mechanics challenges using precise, practical mathematical methods and building strong intuition for real-world applications.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course equips you with essential techniques for Gaussian integrals, analytic continuation, ladder operator algebra, dimensionless Schrödinger equations, x⁴ normal ordering, non-degenerate perturbation theory, series expansions, and asymptotic analysis to determine reliable first-order corrections in practical computations.
Elevify advantages
Develop skills
- Master Gaussian integrals for oscillator norms using complex parameters.
- Apply ladder operators to construct eigenstates and compute x, p, number operators.
- Normal-order x⁴ to simplify vacuum and excited-state expectations.
- Implement perturbation theory for first-order energy shifts in anharmonic oscillators.
- Rescale Schrödinger equations into stable, dimensionless forms for numerical work.
Suggested summary
Before starting, you can change the chapters and 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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