Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Principles of Quantum Mechanics · Problem 2.7.5
All Is Not Well with Classical Mechanics — R. Shankar
Physics — Quantum Mechanics · canonical-transformations
Problem Show that the polar variables ρ = ( x 2 + y 2 ) 1 / 2 \rho = (x^2 + y^2)^{1/2} ρ = ( x 2 + y 2 ) 1/2 ϕ = tan − 1 ( y / x ) \phi = \tan^{-1}(y/x) ϕ = tan − 1 ( y / x ) p ρ = e ^ ρ ⋅ p = x p x + y p y ( x 2 + y 2 ) 1 / 2 , p ϕ = x p y − y p x ( = l z ) p_\rho = \hat{e}_\rho \cdot \mathbf{p} = \frac{xp_x + yp_y}{(x^2+y^2)^{1/2}}, \qquad p_\phi = xp_y - yp_x\ (=l_z) p ρ = e ^ ρ ⋅ p = ( x 2 + y 2 ) 1/2 x p x + y p y , p ϕ = x p y − y p x ( = l z ) e ^ ρ \hat{e}_\rho e ^ ρ Browse the problem library