Quantum Mechanics Answers

A particle is being rotated in a centrifuge which has a radius of 5.0 m. If the 

particle’s centripetal acceleration is 4 g, determine its speed. What is the time period 

of its motion?

 A satellite of mass 2500 kg is orbiting the Earth in an elliptical orbit. At the apagee, the 

altitude of the satellite is 3000 km, while at the perigee its altitude is 1000 km. Calculate 

the energy and angular momentum of the satellite and its speed at the apagee and perigee.

 A particle of mass 3m initially moving with a speed u in the positive x-direction 

collides with a second particle of mass m moving in the opposite direction with an 

unknown speed v. After collision the mass 3m moves along the negative y-direction 

with a speed u/2 and the mass m moves with a speed v in a direction making an angle 

of 45˚ with the positive x-direction. Determine v and v in units of u. Is the collision 

elastic?

A disc rotates with a period of 0.50s. Its moment of inertia about its axis of rotation is 0.08 Kg m²

. A small mass is dropped onto the disc and rotates with it. The moment of 

inertia of the mass about the axis of rotation is 0.02 kg m²

. Determine the final period 

of the rotating disc and mass system.

A merry-go-round is initially at rest. On being given a constant angular acceleration it 

reaches an angular speed of 

1 0.50 rad/sin 10.0 s. At t = 10.0 s, determine the 

magnitude of: (i) the angular acceleration of the merry-go-round ; (ii) the linear velocity 

of a child sitting on the merry-go-round at a distance of 3.0 m from its centre; (iii) the 

tangential acceleration of the child; (iv) the centripetal acceleration of the child; and 

(v) the net acceleration of the child.

Show that I;(cos p – sin p +2i sin o cos ) = 242, where is the azimuthal angle.

A particle of mass mis fixed at one end of a rigid rod of negligible mass and length R The other end of the rod rotates in the xy plane about a bearing located at the origin, whose axis is in the z-direction. (a) Write the system's total energy in terms of its angular momentum L. (b) Write down the time-independent Schrödinger equation of the system Calculate the energy eigenvalues of an axially symmetric rotator and find the degeneracy of each energy level (i.c., for each value of the azimuthal quantum number m, find how many states (1. m) correspond to the same energy). We may recall that the Hamiltonian of an axially symmetric rotator is given by 2+2; 21: where and I2 are the moments of inertia. (b) From part (a) infer the energy eigenvalues for the various levels of I = 3. (c) In the case of a rigid rotator (ie, h = h = 1), find the energy expression and the corresponding degeneracy relation (d) Calculate the orbital quantum number and the corresponding energy degeneracy for a rigid rotator where the magnitude of the total angular momentum is 561.

Consider the operator Å= }(İxjy + JyJ). (a) Calculate the expectation value of  and à with respect to the state | j, m). (b) Use the result of (a) to find an expression for A in terms of: j4, j2, P, Ϊ, Ĵª.

Consider the operator Å= }(İxjy + JyJ). (a) Calculate the expectation value of  and à with respect to the state | j, m).

(b) Use the result of (a) to find an expression for A in terms of: j4, j2, P, Ϊ, Ĵª.

Find the ground-state electron energy by substituting the radial wave function, 𝑅(𝑟)= 2𝑎𝑜3/2𝑒−𝑟𝑎𝑜⁄ that corresponds to 𝑛 = 1,𝑙 = 0, into radial equation for hydrogen atom.