6. The expectation value of a function f(x) of x when the wave function depends only on x is given by ⟨f(x)⟩ = (A)(B)(C)(D)(E)

5. Because the factor ℏ on the right side of Heisenberg's uncertainty principle has units of joule-seconds, it suggests that the energy of a system also has uncertainty. The uncertainty in energy depends on the length of the time interval during which a system exists. ΔEΔt ≥ ℏ/4π. Suppose an unstable mass is produced during a high-energy collision such that the uncertainty in its mass is me/100 (me = 9.11 × 10⁻³¹ kg). How long will this particle exist? (A) 8.1 × 10⁻¹⁹ s (B) 2.3 × 10⁻²³ s (C) 1.0 × 10¹⁵ s (D) 1.2 × 10¹³ s (E) 6.4 × 10⁻²⁰ s

6. The expectation value of a function f(x) of x when the wave function depends only on x is given by ⟨f(x)⟩ =
(A)
(B)
(C)
(D)
(E)

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