Question
In: Physics
Classical mechanics - upper level task 1. A particle of mass m, in one dimension, moves...
Classical mechanics - upper level
task 1. A particle of mass m, in one dimension, moves in the field of force constant F.
Canonical transformation is:
q (t) → Q (t) = q (t + τ) p (t) → P (t) = p (t + τ) (1)
Find the derivative function F2 (q, P) ,
then linearize it by keeping only the linear contributions in
τ.
Shoe that f2 (q, P), the contribution within F2 that multiplies
τ corresponds to the Hamiltonian of the system.
Assume that the particle is initially dormant in its origin.
Task 2.
Show that for functions f, g is:
{f (qi), g (qj )} = 0,
{f (pi), g (pj )} = 0
{f (qi), g (pj )} = 0 for i different than j
Solutions
genius_generous answered 1 year agoRelated Solutions
A particle of mass ? moves in one dimension along the ?- axis. Its potential energy...
A particle of mass ? moves in one dimension along the ?- axis.
Its potential energy is given by ?(?) = ??3 − ??, where ? and ? are
positive constants.
(a) Calculate the force on the particle, ?(?). Find the
position of all equilibrium points and identify them as stable or
unstable.
(b) Draw an energy diagram showing the potential energy U, the
kinetic energy K, and the total mechanical energy E for bound
motion. Show the location of...
A particle with mass m and energy E is moving in one-dimension from right to legt....
A particle with mass m and energy E is moving in one-dimension
from right to legt. It is incident on the step potential V(x)=0 for
x<0 nd V(x)=V0 for x>0 where E>V0>0. Find the
reflection coefficient R in terms of m,E and V0, and h-bar.
A particle with mass m moves on the surface of a cylinder with radius R. At...
A particle with mass m moves on the surface of a cylinder with
radius R. At the same time, the force F = -kr on the particle
affects it through the z axis. Using the z-and θ generalized
coordinates, find the system's hamitonians. Solve the Hamilton
equation after defining the conservative quantities.
A material particle with mass M moves under the gravitational effect of the earth. Solve the...
A material particle with mass M moves under the gravitational
effect of the earth. Solve the Hamilton-jacobi equation of the
particle.
A particle of mass m moves under the influence of gravity g on the inner surface...
A particle of mass m moves under the influence of gravity g on
the inner surface of a smooth cone of half-angle α. The axis of the
cone is vertical, with its vertex downward. (a) Find the
equation(s) of constraint of the system. (b) Find Lagrange’s
equations of motion using the method of undetermined multipliers.
(c) Determine the condition on the angular velocity ω such that the
particle can describe a horizontal circle at a height h above the
vertex.
A material particle with mass M moves under the gravitational effect of the earth. Solve the...
A material particle with mass M moves under the gravitational
effect of the earth. Solve the Hamilton-jacobi equation of the
particle.
particle of mass m, which moves freely inside an infinite potential well of length a, is...
particle of mass m, which moves freely inside an infinite
potential well of length a, is initially in the state Ψ(x, 0) = r 3
5a sin(3πx/a) + 1 √ 5a sin(5πx/a). (a) Normalize Ψ(x, 0). (b) Find
Ψ(x, t). (c) By using the result in (b) calculate < p2 >. (d)
Calculate the average energy
A particle of mass M moves along a straight line with initial speed vi. A force...
A particle of mass M moves along a straight line with initial
speed vi. A force of magnitude Fpushes the particle a distance D
along the direction of its motion.
A) Find vf, the final speed of the particle after it has
traveled a distance D. Express the final speed in terms of vi, M,
F, and D.
B) By what multiplicative factor RK does the initial kinetic
energy increase, and by what multiplicative factor RW does the work
done...
QUANTUM MECHANICS-upper level In the harmonic oscillator problem, the normalized wave functions for the ground and...
QUANTUM MECHANICS-upper level
In the harmonic oscillator problem, the normalized wave
functions for the ground and first excited states are ψ0 and ψ1.
Using these functions, at some point t, a wave function u = Aψ0 +
Bψ1 is constructed, where A and B are real numbers.
(a) Show that the average value of x in the u state is generally
non-zero.
(b) What condition A and B must satisfy if we want the function u
to be normalized?
(c)...
Consider a particle of mass m confined to a one-dimensional box of length L and in...
Consider a particle of mass m confined to a
one-dimensional box of length L and in a state with normalized
wavefunction. For a partide in a box the energy is given by
En =
n2h2/8mL2
and, because the potential energy is zero, all of this energy is
kinetic. Use this observation and, without evaluating any
integrals, explain why < px2>=
n2h2/4L2
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- 1- Briefly distinguish Primary data and secondary data? 2- Discuss the Marketing MEMO?
- In a responsibility accounting reporting system, as one moves up each level of responsibility in information....
- It is often said that control is largely an illusion. For example, in traditional classrooms many...
- The molar enthalpy of a binary liquid system of species 1 and 2 at fixed T...
- JAVA I need to write a code that calculates mean and standard deviation using arrays and...
- This problem is based on the transactions for the Sweet Homes Company in your text. Prepare...
- Time value Personal Finance Problem You have $1,800 to invest today at 8% interest compounded annually....
ADVERTISEMENT