write the kinetic energy operator for a three particle, two dimensional system
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write the kinetic energy operator for a three particle, two dimensional system

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- Obtain the equations of motion for the motion of a particle of mass m in a potential V(x, y, z) in spherical polar coordinates. Also write down the equations of motion if the force is central.Problem 9. For a system described by the Hamiltonian H = p°/2m + V(x), obtain an expression for d (p/2m)Idt. Discuss the relation of your result to the classical work-energy theorem.5. Consider two identical linear oscillators having a spring constant k. The interaction potential is H = Ax,x, where x, and x, are the coordinates of the oscillators. Obtain the energy eigenvalues.
- Problem 2: A student pushes a baseball of m = 0.18 kg down onto the top of a vertical spring that has its lower end fixed to a table, compressing the spring a distance of d = 0.14 meters from its equilibrium length. The spring constant of the spring is k = 740 N/m. Let the gravitational potential energy be zero at the position of the baseball in the compressed spring. Randomized Variables m = 0.18 kg k = 740 N/m d = 0.14 mConsider two particles m1 and m2. Let mlbe confined to move on a circle of radius R1 in the z-0 plane and centered at x-0, y-0. Let m2 be confined to move on a circle of radius R2 in the z-a plane and centered at x-0, y-0. A massless spring of spring constant C is joining the two particles. www Set up the Lagrangian for the system. Set up the equations of constraints. Set up the Lagrange equations using Lagrange multipliers.derive and show working out please
- Find C please step by step .Minimal use of the calculator pleaseThe Newton–Raphson method for finding the stationary point(s) Rsp of a potential energy surface V is based on a Taylor-series expansion around a guess, R0. Similarly, the velocity Verlet algorithm for integrating molecular dynamics trajectories [xt, vt] is based on a Taylor-series expansion around the initial conditions, [x0, v0]. Both of these methods rely strictly on local information about the system. How many derivatives do we need to compute in order to apply them?The Brachistochrone Problem: Show that if the particle is projected withan initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloidpassing through the two points with a cusp at a height z above the initialpoint given by v02 = 2gz.
- 5. Consider the two state system with basis |+) which diagonalizes the Pauli matrix 03. Generally the state of the system at time t can be written as |W(t)) = c+(t)|+) + c_(t)|-). (i) For the Hamiltonian of the system, first take H = functions c+(t) given the initial condition that at time t = 0 Eo03. Solve for the coefficient |W(0)) = |-).For a one dimensional system, x is the position operator and p the momentum operator in the x direction.Show that the commutator [x, p] = ihFor the potential-energy functions shown below, spanning width L, can a particle on the left side of the potential well (x 0.55L)? If not, why not? b. c. 0 a. 0o 00 E E E-