Physical Math Course
This Physical Mathematics 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.

from 4 to 360h flexible workload
certificate valid in your country
What will I learn?
Explore practical tools for Gaussian integrals, analytic continuation, and ladder operator algebra in the Physical Mathematics Course. Tackle dimensionless Schrödinger equations, x⁴ normal ordering, non-degenerate perturbation theory, series expansions, and asymptotic analysis to determine 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 for 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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