Hamiltonian Formulation 1. Motivation
Appropriate for application to statistical mechanics and quantum mechanics
Newtonian and Lagrangian viewpoints take the qi as the fundamental variables
- N-variable configuration space
- appears only as a convenient shorthand for dq/dt
- working formulas are 2nd-order differential equations
Hamiltonian formulation seeks to work with 1st-order differential equations
- 2N variables
- treat the coordinate and its time derivative as independent variables
- appropriate quantum-mechanically