Physical Math Course
This Physical Mathematics Course teaches Gaussian integrals, ladder operators, and perturbation theory. Learners gain skills in dimensionless Schrödinger equations, normal ordering, and assessing series expansions for reliable quantum calculations in oscillator systems.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Explore practical tools 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 mechanics computations.
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 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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