1. Find the expectation value for position and kinetic energy. Can these properties be measured simultaneously? 2. Find the expectation value for momentum and kinetic energy. Can these properties be measured simultaneously?

A) Explain what the difference is between the “center of mass” and the “centroid” of an object. B) how is moment of inertia related to kinetic energy? C) Explain what a joint probability density function is supposed to measure.

10. A particle is represented (at time t = 0) by the wave function ¥(x,0) = {4(a² ¯ 0, JA(a²-x²), if- a ≤x≤+a otherwise (a) Determine the normalization constant A. (b) What is the expectation value of x (at time t = 0)? d (c) What is the expectation value of p (at time t = 0)? (Note that you cannot get it from p = m² .Why dt not?) (d) Find the expectation value of x². (e) Find the expectation value of p².

0 A physical system is described by a two-dimensional vector space with Hamiltonian operator Ĥ given by Ĥ = (_) where a is a constant. At time t = 0, the system is prepared in state (t = 0)) = -i2.5 0 determine the expectation value (Ŝ) at time t = πħ/(4x). O a. 2.17 O b. -2.50 O c. -1.25 O d. 2.50 O e. 5.00 0 (¹). For operator $ = (2 i2.5