2. Consider a gas of N spinless non-relativisitic bosons trapped in a 2-dimensional harmonic potential V = {mw2(x2 + y2)

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2 Consider A Gas Of N Spinless Non Relativisitic Bosons Trapped In A 2 Dimensional Harmonic Potential V Mw2 X2 Y2 1 (102.68 KiB) Viewed 46 times

2. Consider a gas of N spinless non-relativisitic bosons trapped in a 2-dimensional harmonic potential V = {mw2(x2 + y2). The single-particle energy levels are (nz + ny + 1)ħw. (Laboratory BECs are produced in traps.) a) Optional By considering the number of states with energy between ε and € + de, show that in the continuum approximation, the density of states in energy is g(e) = (€ – ħw) for ε > ħw. (ħw)2 [ Hint: we are working directly with energies here, the momentum or wave number do not play a role in the harmonic oscillator. It may help to consider a 2D grid of energy states (rather than as before, momentum states).]