1. Suppose that two non-interacting particles are confined in a harmonic potential of natural frequency w (u = /k/m) (a)

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1 Suppose That Two Non Interacting Particles Are Confined In A Harmonic Potential Of Natural Frequency W U K M A 1 (42.38 KiB) Viewed 31 times

1. Suppose that two non-interacting particles are confined in a harmonic potential of natural frequency w (u = /k/m) (a) Ignore spin. Find the wave function, energy and degeneracy of the ground state, Ist excited state and 2nd excited state for "distinguishable particles”, bosons, and fermions, respectively. (b) Now, suppose that particles have spin 1/2. Find the wave function, energy and degeneracy of the ground state, Ist excited state and 2nd excited state for "distinguishable particles" and “identical particles", respectively. (c) Do the same as (b), supposing that particles have spin 1. Note: For (a), refer to Example 5.1 and Problem 5.5(b) of Griffiths 3rd edition, where two non-interacting particles are confined in the infinite square well potential. For (b) and (c), refer to Problem 5.9 (a) and (b) of Griffiths, respectively. Suggestion: Use the notation na nzls m), where Unanz is defined in Example 5.1 and is m) in Section 4.4.3 of Griffiths. For example, Is = 3 m = 0) is shown in the first equation of p. 179 of Griffiths.