Apply the generalised uncertainty principle to and

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · The formalism of quantum mechanics

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Observables, commutators and the uncertainty relations

Problem

Apply the generalised uncertainty principle to A^=x^\hat A = \hat x and B^=H^\hat B = \hat H, using [x^,H^]=iℏp^/m[\hat x,\hat H] = i\hbar\hat p/m derived in this chapter, to find a bound on Δx ΔH\Delta x\,\Delta H. For a state with ⟨p⟩=0\langle p\rangle = 0, what does this bound say, and how does that differ from the x^\hat x-p^\hat p case?

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