Principles of Quantum Mechanics · Problem 2.3.1
Review of Classical Mechanics — R. Shankar
Physics — Quantum Mechanics · two-body-problem-lagrangian
Problem
Derive Eq. (2.3.6) from (2.3.5) by changing variables.Intuitive explanation
This is a change-of-variables problem in quantum mechanics—the kind where a clever substitution transforms one integral or differential equation into another form. The key insight is to identify which new variable (often a dimensionless combination or a shifted coordinate) will simplify the structure and reveal a standard form. Once you spot the right substitution and carefully transform both the differential operator and the limits, the algebra usually flows naturally and Eq. (2.3.6) emerges as the cleaner result.
Intuitive explanation
This is a change-of-variables problem in quantum mechanics—the kind where a clever substitution transforms one integral or differential equation into another form. The key insight is to identify which new variable (often a dimensionless combination or a shifted coordinate) will simplify the structure and reveal a standard form. Once you spot the right substitution and carefully transform both the differential operator and the limits, the algebra usually flows naturally and Eq. (2.3.6) emerges as the cleaner result.