Question

(a) Show that the Hamiltonian for the quantum harmonic oscillator problem, 1 A = 5 mw?22 Ø 2 2m can be expressed solely in te

(b) The ground-state (i.e. lowest-energy) wavefunction for the quantum harmonic oscillator problem is 4.(x) = A exp[-mwx2/(2h

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solution @ ata = 1 2 2 mwa x + i w h w įw рх 2 .pt 2 2m mw22 2 ط tw н iw it tw & ħw cata) À I to 11 2 → ħw (at at 1 ) = 2 (bH Yn En Yr Hep = E, V Use at Yn Infi twlata +1) 42 = E, Y » to at als + 29 ] = Et 4 h = √nti e o & a%= 5nl mal w [ I up ] = E

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