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.

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

Assume this car is driven off a cliff . how many arrows of force need to be drawn in the free body diagram? assume no air resistance -five -one -three -four

What is the name for the remnant of an asymptotic giant that has lost its shells? black dwarf white dwarf yellow giant black hole