Physical Math Course
Dive into advanced physical mathematics with this course, covering Gaussian integrals, ladder operators, normal ordering of x⁴, perturbation theory for anharmonic oscillators, and rescaled Schrödinger equations. Gain confidence in solving quantum mechanics problems through precise tools and asymptotic evaluations for reliable real-world applications.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course equips learners 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 validate first-order corrections in 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.
- Implement perturbation theory for first-order energy corrections in oscillators.
- Rescale Schrödinger equations into stable, dimensionless numerical forms.
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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