Physical Math Course
This Physical Math Course equips you with essential tools for Gaussian integrals, ladder operators, and perturbation theory. Gain confidence in handling Schrödinger equations and quantum oscillator systems through precise mathematical techniques and practical applications in real-world quantum problems.

4 to 360h flexible workload
certificate valid in your country
What will I learn?
Explore practical tools for Gaussian integrals, analytic continuation, ladder operator algebra, dimensionless Schrödinger equations, x⁴ normal ordering, and non-degenerate perturbation theory, while evaluating series expansions and asymptotic behavior for reliable first-order corrections.
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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