Physical Math Course
This Physical Mathematics Course teaches Gaussian integrals, ladder operators, normal ordering, perturbation theory, and rescaling of Schrödinger equations. Students gain skills to solve quantum oscillator problems confidently using precise mathematical techniques and build strong intuition for physical applications in quantum mechanics.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Explore practical methods in physical mathematics, covering 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 with complex parameters.
- Use ladder operators to build eigenstates and evaluate x, p, number operators.
- Normal-order x^4 to compute vacuum and excited-state expectations.
- Apply perturbation theory for first-order energy shifts in anharmonic oscillators.
- Rescale Schrödinger equations into dimensionless, stable numerical models.
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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