Physical Math Course
This Physical Math Course teaches Gaussian integrals, ladder operators, normal ordering of x⁴, and non-degenerate perturbation theory. Learners handle dimensionless Schrödinger equations, series expansions, and asymptotic behavior to confidently solve quantum oscillator problems with precise tools.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Gain practical skills in Gaussian integrals, analytic continuation, ladder operator algebra, dimensionless Schrödinger equations, x⁴ normal ordering, and perturbation theory. Evaluate series expansions and asymptotics to ensure reliable 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, and number operators.
- Normal-order x^4 to streamline vacuum and excited-state expectation values.
- Apply perturbation theory for first-order energy shifts in anharmonic oscillators.
- Rescale Schrödinger equations into 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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