Consider two non-interacting particles in one-dimension. Both particles have mass, m, and are subject to a harmonic potential well with spring constant, k. The quantum dynamics of each particle is characterized by the natural frequency, w = Ym · Answer the following questions: (а) ) Consider the case that the particles both have spin 0, and they are distinguishable. Starting with and counting the ground state, what are the first three lowest energies that can be measured for the non-interacting two-particle system? List the energies from lowest (ground state) to highest (go up to the 2nd excited state) and also specify the degeneracy of each energy level. You must show all work to justify your answers. (b) Answer the same question given in part (a) for indistinguishable particles of spin ½. (c) Answer the same question given in part (a) for indistinguishable particles of spin 1.
Consider two non-interacting particles in one-dimension. Both particles have mass, m, and are subject to a harmonic potential well with spring constant, k. The quantum dynamics of each particle is characterized by the natural frequency, w = Ym · Answer the following questions: (а) ) Consider the case that the particles both have spin 0, and they are distinguishable. Starting with and counting the ground state, what are the first three lowest energies that can be measured for the non-interacting two-particle system? List the energies from lowest (ground state) to highest (go up to the 2nd excited state) and also specify the degeneracy of each energy level. You must show all work to justify your answers. (b) Answer the same question given in part (a) for indistinguishable particles of spin ½. (c) Answer the same question given in part (a) for indistinguishable particles of spin 1.
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Transcribed Image Text:Consider two non-interacting particles in one-dimension. Both particles have mass, m,
and are subject to a harmonic potential well with spring constant, k . The quantum dynamics of each
particle is characterized by the natural frequency, w = V%m · Answer the following questions:
(а)
) Consider the case that the particles both have spin 0, and they are distinguishable. Starting
with and counting the ground state, what are the first three lowest energies that can be measured
for the non-interacting two-particle system? List the energies from lowest (ground state) to highest
(go up to the 2nd excited state) and also specify the degeneracy of each energy level. You must
show all work to justify your answers.
(b)
Answer the same question given in part (a) for indistinguishable particles of spin ½.
(c)
Answer the same question given in part (a) for indistinguishable particles of spin 1.
Hint: You can do all three parts by drawing pictures. No need to employ a general formula.
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