Question

(a) Find the magnitude of the momentum of a particle in a box in its nth state. (b) The minimum change in the particle's momentum that a measurement can cause corresponds to a change of ±1 in the quantum number n. If Δx = L, show that ΔpΔx ≥ ħ/2.

Name: afind the magnitude of the momentum of a particle in a box in its nth state b the minimum change in the particles momentum that a measurement can cause corresponds to a change of pm 1 in the 89972
Uploaded: 2024-07-29T23:06:42-08:00
Duration: 2 min 41 s
Channel: Adi S
Description: afind the magnitude of the momentum of a particle in a box in its nth state b the minimum change in the particles momentum that a measurement can cause corresponds to a change of pm 1 in the 89972

          (a) Find the magnitude of the momentum of a particle in a box in its nth state.
(b) The minimum change in the particle's momentum that a measurement can cause corresponds to a change of ±1 in the quantum number n. If Δx = L, show that ΔpΔx ≥ ħ/2.

Added by Maria E.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

07/29/2024

Step 1

The particle's wavefunction must satisfy the boundary conditions, leading to quantized energy levels. The wavefunction for the nth state is given by: \[ \psi_n(x) = \sqrt{\frac{2}{L}} \sin\left(\frac{n\pi x}{L}\right) \] where \( n \) is a positive integer Show more…

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(a) Find the magnitude of the momentum of a particle in a box in its nth state. (b) The minimum change in the particle's momentum that a measurement can cause corresponds to a change of ±1 in the quantum number n. If Δx = L, show that ΔpΔx ≥ ħ/2.