the following problems pertain to a wavefunc- tion of the form y(x) = e-x2 (which is not yet normalized) (a) sketch ψ(x) (over a range of-2 < x < 2). (b) normalize ψ(x). (c) what is the probability that the particle will be found at some positive value of x? (d) evaluate the expectation values 。) and (x2), and use these to determine the uncertainty in the particle's position ox = (e) evaluate the uncertainty in the particles momentum σpx-vod-px)2, and show that this is exactly equal to the minimum value allowed by the position-momentum uncertainty relation (eq. 6.42) 6. determine the conditions under which a wave- function of the form ψ(x)=e-ar' will be an eigenfunction of the operator a= bx2, where a and b are positive real num- bers, and express the resulting eigenvalue in terms of b.