Consider two identical spin particles in a harmonic oscillator potential. So that the Hamiltonian takes...

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Consider two identical spin ½ particles in a harmonic oscillator potential. So that the Hamiltonian takes the form P? P?2 +mw?(r – r2)² 1 H = + 2m 2m Assume that the two-particle system has zero center-of-mass momentum, and that the two particles are in l=0 states. a) Write down the ground state wave function, including the spin state and also determine degeneracy. b) Write down the first excited states in the singlet and the triplet spin states. Now determine degeneracy. c) Assume that there is a short-range interaction between the particles, which in the l=0 state can be approximated by C[, Calculate the effect of this perturbation on the states obtained in (b). Consider two identical spin ½ particles in a harmonic oscillator potential. So that the Hamiltonian takes the form P? P?2 +mw?(r – r2)² 1 H = + 2m 2m Assume that the two-particle system has zero center-of-mass momentum, and that the two particles are in l=0 states. a) Write down the ground state wave function, including the spin state and also determine degeneracy. b) Write down the first excited states in the singlet and the triplet spin states. Now determine degeneracy. c) Assume that there is a short-range interaction between the particles, which in the l=0 state can be approximated by C[, Calculate the effect of this perturbation on the states obtained in (b).

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AE r With the systems center of mass at rest the twobody problem reduces to a onebody problem whose ... View the full answer