Physical Math Course
Dive into advanced physical mathematics with this course, mastering Gaussian integrals, ladder operators, normal ordering, perturbation theory, and rescaled Schrödinger equations. Gain the confidence and precise tools to solve real-world quantum mechanics problems involving oscillator systems and beyond.

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, and non-degenerate perturbation theory, including series expansions and asymptotic analysis to validate first-order corrections in practical quantum calculations.
Elevify advantages
Develop skills
- Master Gaussian integrals for oscillator norms using complex parameters.
- Harness ladder operators to construct eigenstates and compute x, p, number operators.
- Normal-order x⁴ to simplify vacuum and excited-state expectations.
- Apply perturbation theory for first-order energy shifts in anharmonic oscillators.
- Rescale Schrödinger equations into stable, dimensionless numerical models.
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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