Due April 19th, 2019 1. (3 pts) Consider two particles of mass mi and m2 (in one dimension) that ...
A system consists of two particles of mass mi and m2 interacting with an interaction potential V(r) that depends only on the relative distancer- Iri-r2l between the particles, where r- (ri,/i,21) and r2 22,ひ2,22 are the coordinates of the two particles in three dimensions (3D) (a) /3 pointsl Show that for such an interaction potential, the Hamiltonian of the system H- am▽ri _ 2m2 ▽22 + V(r) can be, put in the form 2M where ▽ and ▽ are the...
Problem 3. Consider two atoms with masses mi and m2, each moving along the x-direction, and that are connected by a harmonic spring with spring constant k and equilibrium length lo: mi m2 Ömimo → X1 X2 The Hamiltonian operator for this system is ÎN = Pí 1 2 1 2 +5k (ĉ2 – ĉ1 – 10)? 2m2' 2" 2m, and the time-independent Schrödinger equation for the two-atom wavefunction (x1, x2) is ÊV(21, x2) = EV (21, x2) This equation...
4. Consider two particles of masses my and m2 and positions rı and r2 respectively. Suppose m2 exerts a force F on mı. Suppose further that the two particles are in a uniform gravitational field g. (a) Write down the equations of motion for the two particles. (b) Show that the equations of motion can be written as MR = Mg ur = F where M is the total mass, R is the centre of mass, he is the reduced...
Question 1 (8 marks in total) The deuteron is a bound state of a proton and a neutron. Treating nucleons as identical particles with spin and isospin degrees of freedom, the total state of the deuteron can be writ- ten space Ψ spin Ψ isospin. The deuteron has a total angular momentum quantum number J - 1 and a total spin S -1. Our goal is to determine the parity of the deuteron Q1-1 (1 mark) Show that the possible...