Hamiltonian of a system is given by:
Q: For a one-dimensional system with the Hamiltonian H = p2/2 − 1 / (2 q2), show that there is a…
A: Given that,H=p22-12q2D= pq2-HtWe have Liouville's theorem which is,dFdt = ∂F∂t+F, HHere F = DSo in…
Q: A bead slides without friction down a wire that has a shape y = f(x). (a) Prove that the EOM is (1…
A: Disclaimer: The above problem is a multiple-part problem. It is not indicated which part to be…
Q: Consider a Hamiltonian of the form 0 U H = (5 %) + ^ ( 2 ) B with a value of << 1.
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Q: The Hamiltonian of a two level system is given by - Â = E。[|1X(1| — |2X(2|] + E₁[11X(2| + |2X1|]…
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Q: Show that if the Hamiltonian and a quantity F are constants of motion, then af/at is also a…
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Q: A particle of mass m oscillates in a vertical plane suspended by a massless string that goes through…
A: This is the problem with the simple pendulum with a variable length of the pendulum. That is of…
Q: For motion in a plane with the Hamiltonian H = |p|n − a r−n, where p is the vector of the momenta…
A: Given: The Hamiltonian of the motion in a plane is The operator
Q: Let a two-degree-of-freedom system be described by the Hamiltonian = 1/ (p² + p ²) + V(x, y) and…
A: Given Hamilton : And the potential energy V is a homogeneous function of degree -2 for all
Q: Consider a bead of mass m constrained to move along a vertical hoop of radius R. The hoop is…
A: Given: Bead of Mass "m" Radius "R" To find: (a) How many constraints and generalised coordinates are…
Q: Verify that Y1 and Y1' are eigenfunctions of the 3D Rigid Rotor Hamiltonian.
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Q: The free space Lagrangian for a particle moving in 1D is L (x,x, t) = a) Show that pat = SL = ymv b)…
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Q: The Lagrangian for a particle of mass m at a position i moving with a velocity v is given m -2 by…
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Q: The raising (a) and lowing (a) operators associated with a simple harmonic oscillator Hamiltonian…
A: (a) The commutator of the lowering and raising operators is calculated in the following way.
Q: By applying the methods of the calculus of variations, show that if there is a Lagrangian of the…
A: The hamiltonian principle states that the variation between two points in a conservative system is…
Q: Find the equation of motion and the Hamiltonian corresponding to the Lagrangian L * = {{@, 9)² =…
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Q: Consider the uniform motion of a free particle of mass m. The Hamiltonian is a constant of the…
A: Given: The quantity is given as F(x, p, t) = x − pt/m
Q: A particle of mass m moves in a plane under the influence of a central force that depends only on…
A: According to question body moving in central force so Lagrangian will be, Let the potential is V(r)…
Q: Find the Hamiltonian H for a mass m confined to the x axis and subject to a force Fx = - kx³, where…
A: Answer
Q: A particle of mass m is attracted to a force center with the force of magnitude k/ r2. Use plane…
A: It is given that, a force of magnitude F=kr2 is used to attract a particle of mass m to a force…
Q: A particle of mass m is attracted to a force center with the force of magnitude k/ r2. Use plane…
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Q: What is Hamiltonian cycle?
A: What is hamiltonian cycle.
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- Suppose that you have the Lagrangian L = (;2 + ʻr²) + 20 for a 2D 20 system in plane polar coordinates (r, 0). Determine the Hamiltonian.Consider a particle of mass m moving freely in a conservative force field whose potential function is U. Find the Hamiltonian function and show that the canonical equations of motion reduce to Newton’s equation.The inclination angle of a particle of mass m is adjustable, located on the moving edge. Inclined plane is horizontal at time t = 0 is in position. At t>0 moveable edge of the inclined plante is lifted by constant angular velocity of w to allow mass m to start to moving. Write down the Lagrangian equation of the mass m.
- Write down the Hamiltonian function and Hamilton’s canonical equations for a simple Atwood machine.It has been previously noted that the total time derivative of a functionof qi and t can be added to the Lagrangian without changing the equationof motion. What does such an addition do to the canonical momenta andthe Hamiltonian? Show that the equations of motion in terms of the newHamiltonian reduce to the original Hamilton’s equations of motion.A pendulum consists of a mass m suspended by a massless spring withunextended length b and spring constant k. The pendulum’s point of supportrises vertically with constant acceleration a. (a) Use the Lagrangian method to find the equations of motion. (b) Determine the Hamiltonian and Hamilton’s equations of motion.
- 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.A bead of mass 'm' is constrained to move along a rigid wire having the shape of a rectangular hyperbola. Write the Lagrangian and Lagrange's equation of motion.A bead can slide on a straight wire which is always in the vertical plane. C is point on wire and wire is moving so the line joining origin O and Point C is rotated in the vertical plane with constant angular velocity ω.(a) Find appropriate generalised coordinates, Lagrangian, and the Euler-Lagrange equations and solve it for the position of the bead.(b) Find Hamiltonain. Comment on the total energy of the system.