Question

given that H=1/2mpx^2 + 1/x mw^2x^2 given that m is the effective mass of the oscillator...

given that H=1/2mpx^2 + 1/x mw^2x^2

given that m is the effective mass of the oscillator and v is the frequency and w is the angular frequency defined by w=2piv.

given that (A+) = 2m^(-1/2)(px+1mwx) and (A-) = 2m^(-1.2)(px-imwx)

(a) show that (A+)(A-) = H-1/2hv and (A-)(A+)=H+1/2hv

(b) show that [(A+),(A-)]=-hv anbd that [H,A+]=hvA+ and [H,A-]=-hvA-

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