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a) Reverse the Legendre transformation to derive the properties of L(qi, q˙i, t) from H(qi, pi, t), treating the q˙i as independent quantities, and show that it leads to the Lagrangian equations of motion. (b) By the same procedure find the equations of motion in terms of the function L' (p, p˙ , t) = −p˙iqi − H(q, p, t).

a) Reverse the Legendre transformation to derive the properties of L(qi, q˙i, t) from H(qi, pi, t), treating the q˙i as independent quantities, and show that it leads to the Lagrangian equations of motion. (b) By the same procedure find the equations of motion in terms of the function L' (p, p˙ , t) = −p˙iqi − H(q, p, t).

University Physics Volume 3
University Physics Volume 3
17th Edition
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:William Moebs, Jeff Sanny
Chapter7: Quantum Mechanics
Section: Chapter Questions
Problem 42P: Show that when 1(x,t) and 2(x,t) are solutions to the time-dependent Schrödinger equation and A, B...
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a) Reverse the Legendre transformation to derive the properties of

L(qi, q˙i, t) from H(qi, pi, t), treating the q˙i as independent quantities, and show that it leads to the Lagrangian equations of motion.

(b) By the same procedure find the equations of motion in terms of the
function

L' (p, p˙ , t) = −p˙iqi − H(q, p, t).

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