1. A $^{87}$Rb atom ($$m = 1.44 \times 10^{-25}$$ kg) is trapped by an optical tweezer made with light. The tweezer forms a three-dimensional quantum harmonic oscillator, where the two trapping angular frequencies are $$\omega_x, \omega_y, \omega_z$$ along $$x, y, z$$ respectively. What are the trapping frequencies $$\omega_x/2\pi, \omega_y/2\pi, \omega_z/2\pi$$ if the width of the single atomic wavefunction in the ground state of the trap is $$\sigma_x = 45$$ nm along $$x$$ and $$\sigma_y = 33$$ nm along $$y$$, and $$\sigma_z = 101$$ nm along $$z$$ respectively? (6 pts)
