Check the uncertainty principle for the wave function in Equation 2.132. Calculating (p²) can be tricky, because the derivative of Ψ has a step discontinuity at x = 0. You may want to use the result in Problem 2.23(b). Partial (p²) = (mα/ћ)².

Equation 2.132

Problem 2.23(b)

(b) Let θ(x) be the step function:

(In the rare case where it actually matters, we define θ(0) to be 1/2.) Show that dθ/dx = δ(x) .

Transcribed Image Text:

y(x) = √ma e-ma\x\/h²; ħ E = - ma² 2h² (2.132)