For a quantum particle of mass m in the ground state of a square well with length L and infinitely high walls, the uncertainty in position is Δx ≈ L. (a) Use the uncertainty principle to estimate the uncertainty in its momentum.(b) Because the particle stays inside the box, its average momentum must be zero. Its average squared momentum is then ⟨p2⟩ ≈ (Δp)2. Estimate the energy of the particle. (c) State how the result of part (b) compares with the actual ground-state energy.
For a quantum particle of mass m in the ground state of a square well with length L and infinitely high walls, the uncertainty in position is Δx ≈ L. (a) Use the uncertainty principle to estimate the uncertainty in its momentum.(b) Because the particle stays inside the box, its average momentum must be zero. Its average squared momentum is then ⟨p2⟩ ≈ (Δp)2. Estimate the energy of the particle. (c) State how the result of part (b) compares with the actual ground-state energy.
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For a quantum particle of mass m in the ground state of a square well with length L and infinitely high walls, the uncertainty in position is Δx ≈ L. (a) Use the uncertainty principle to estimate the uncertainty in its momentum.
(b) Because the particle stays inside the box, its average momentum must be zero. Its average squared momentum is then ⟨p2⟩ ≈ (Δp)2. Estimate the energy of the particle. (c) State how the result of part (b) compares with the actual ground-state energy.
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