Physical Math Course
Dive into this Physical Mathematics Mastery Course to gain expertise in Gaussian integrals, ladder operators, and perturbation theory. Develop strong intuition for Schrödinger equations and quantum oscillator systems, empowering you to solve real-world quantum challenges confidently using precise mathematical techniques and reliable methods.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This Physical Mathematics Mastery Course equips you with essential tools for Gaussian integrals, analytic continuation, and ladder operator algebra. You will tackle dimensionless Schrödinger equations, normal ordering of x⁴ terms, and non-degenerate perturbation theory, while evaluating series expansions and asymptotic behaviour to determine reliable first-order corrections in practical computations.
Elevify advantages
Develop skills
- Master Gaussian integrals for computing oscillator norms with complex parameters.
- Harness ladder operators to construct eigenstates and compute x, p, and number operators.
- Normal-order x⁴ expressions to simplify vacuum and excited-state expectation values.
- Implement perturbation theory to calculate first-order energy shifts in anharmonic oscillators.
- Rescale Schrödinger equations into dimensionless forms for stable numerical solutions.
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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