Lecture Note
University:
Santa Fe CollegeCourse:
PHY 2048 | General Physics 1 with CalculusAcademic year:
2024
Views:
257
Pages:
7
Author:
Jabin F.
= (2/a) ∫₀ᵃ sin(nπx/a) (ih/dx) sin(nπx/a) dx
= 0 ψₙ(x) = √(2/a) sin(nπx/a) Eigenfunction of linear momentum operator
= Σₙ pₙλₙ = (i/2) (nπħ/a) + (i/2) (-nπħ/a)
= 0
= (2/a) ∫₀ᵃ sin(nπx/a) (-ħ²/dx²) sin(nπx/a) dx
= +ħ² (2/a) (n²π²/a²) ∫₀ᵃ sin²(nπx/a) dx
= (n²π²ħ²/a²) x (2/a) ∫₀ᵃ sin²(nπx/a) dx
= n²π²ħ²/a²
=> = 2m = 2m = n²π²ħ²/a²
Now, δx = √( -
²) ΔP = nπħ/a Δx.ΔP = nπħ√(1/12 - 1/2n²π²) Δx.ΔP = 0.568ħ for n = 1
Probability Density
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