Question

Consider a particle moving in one dimension, with coordinate x and velocity ˙x. Suppose that the particle moves in a potential U(x) = 1/2 (kx^2) (a) (2 points) Find the canonical momentum p ≡ ∂L/∂x˙. (b) Find the Hamiltonian function H(p, x). (c) Obtain the canonical (Hamilton) equations for ˙p and ˙x. (d) Use the result of parts (b) and (c) to show explicitly that H is a conserved quantity. .

Name: consider a particle moving in one dimension with coordinate x and velocity x suppose that the particle moves in a potential ux 12 kx2 a 2 points find the canonical momentum p lx b find the hamiltonian
Uploaded: 2023-02-11T02:32:16-08:00
Duration: 2 min 57 s
Channel: Timothy James
Description: consider a particle moving in one dimension with coordinate x and velocity x suppose that the particle moves in a potential ux 12 kx2 a 2 points find the canonical momentum p lx b find the hamiltonian

          Consider a particle moving in one dimension, with coordinate x and velocity ˙x.
Suppose that the particle moves in a potential
U(x) = 1/2 (kx^2)
(a) (2 points) Find the canonical momentum p ≡ ∂L/∂x˙.
(b) Find the Hamiltonian function H(p, x).
(c) Obtain the canonical (Hamilton) equations for ˙p and ˙x.
(d) Use the result of parts (b) and (c) to show explicitly that H is a
conserved quantity.

.

Added by Priyanka T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Timothy James

02/11/2023

Step 1

Hence, p = -kx^2. Show more…

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Consider a particle moving in one dimension, with coordinate x and velocity ˙x. Suppose that the particle moves in a potential U(x) = 1/2 (kx^2) (a) (2 points) Find the canonical momentum p ≡ ∂L/∂x˙. (b) Find the Hamiltonian function H(p, x). (c) Obtain the canonical (Hamilton) equations for ˙p and ˙x. (d) Use the result of parts (b) and (c) to show explicitly that H is a conserved quantity. .