A two-dimensional harmonic oscillator has angular frequencies ωx=2ωy=6.5×10¹⁴ rad/s. Find the wavelength for x-polarized excitation from the ground state to the next allowed state, as a number ×10⁻⁶ m (one decimal place). c=3.0×10⁸ m/s.
For x-polarized light, the dipole operator x changes nx by ±1 and leaves ny unchanged. From the ground state the transition is (0,0)→(1,0), with ΔE=ℏωx. Thus λ=hc/ΔE=2πc/ωx=2π(3×10⁸)/(6.5×10¹⁴)=2.90×10⁻⁶ m. Enter 2.9.
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