Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Students have asked these similar questions
Prove the following: if the Hamiltonian is independent of time, then ∆E doesn't change in time. Show work and be explicit to prove the statement.
Two mass points of mass m1 and m2 are connected by a string passing through a hole in a smooth table so that m1 rests on the table surface and m2 hangs suspended. Assuming m2 moves only in a vertical line, what are the generalized coordinates for the system? Write the Lagrange equations for for the system and, if possible, discuss the physical significance any of them might have. Reduce the problem to a single second-order differential equation and obtain a first integral of the equation. What is its physical significance? (Consider the motion only until m1 reaches the hole.)
Consider a particle of spin s = 3/2.
(a) Find the matrices representing the operators S^
x
, S^
y
,S^
z
,
^
Sx
2
and ^
S y
2 within the basis of
^
S
2
and S^
z
(b) Find the energy levels of this particle when its Hamiltonian is given by
^H=
ϵ 0
h
2
( Sx
2−S y
2
)−
ϵ 0
h
( S^
Z )
where ϵ 0
is a constant having the dimensions of energy. Are these levels degenerate?
(c) If the system was initially in an eigenstate Ψ0=(
1
0
0
0)
, find the state of the system at time
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