Physical Math Course
This Physical Mathematics Course equips you with mastery of Gaussian integrals, ladder operators, and perturbation theory. Develop intuition for Schrödinger equations and oscillator systems, enabling confident handling of real quantum problems using precise mathematical tools.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
The Physical Mathematics Course provides focused, practical tools for managing Gaussian integrals, analytic continuation, and operator algebra via ladder operators. Engage with dimensionless Schrödinger equations, normal ordering of x⁴, and non-degenerate perturbation theory, then evaluate series expansions and asymptotic behaviour to determine reliability of first-order corrections in practical calculations.
Elevify advantages
Develop skills
- Master Gaussian integrals: compute oscillator norms with complex parameters.
- Employ ladder operators: construct eigenstates and evaluate position, momentum, and number operators.
- Normal-order x⁴: simplify vacuum and excited-state expectation values.
- Apply perturbation theory: calculate first-order energy shifts for anharmonic oscillators.
- Rescale Schrödinger equations: formulate dimensionless, numerically stable 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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