Question

The force between two quarks is approximately the same as the spring force (i.e. F = -kr). The potential energy associated with this force is given by U = .5kr^2. Assuming the quarks have equal mass,

Derive expressions for the energy levels and radii of this system. Make sure to box your final answer.

Make a qualitative energy level diagram for this system. Give values for at least the first three levels.

If the system makes a transition from n = 4 to n = 3 what is the wavelength of the emitted photon? You'll have an expression for lambda.

Answer 1

The force between quarks is given by:

So,

or,

or,

We have omitted the minus sign since kinetic energy cant be negative.

Also, given that potential energy is -0.5kr^2.

So, total energy=

or

If the system makes transition from n=4 to n=3, the energy of photon emitted will be:

or,