Estimate the minimum energy of the simple harmonic oscillator allowed by the uncertainty principle.

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Estimate the minimum energy of the simple harmonic oscillator allowed by the uncertainty principle.

Expert Solution
Step 1

Energy of the harmonic oscillator

E=12mω2x2+p22m=12mω2x2+/2x22m=mω2x22+28mx2

Step 2

Differentiate the above equation and equate it to zero to minimize the energy

dEdx=0mω2x+-228mx3=0-228mx3=mω2xx4=222m2ω2x2=2mω

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