Construct quantum mechanical operators in the position representation for the following observables (1) kinetic energy in the y-dimension (2) kinetic energy in the 3-d space (3) the inverse square separation, x2 (4) electric dipole moment in the 3-d space (5) the z-component of the angular momentum

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

Asubject in a clinical research trial experiences a serious, unanticipated adverse drug experience. how should the investigator proceed, with respect to the irb, after the discovery of the adverse event occurrence? a. do not report the adverse drug experience to the irb since it is a common adverse experience.b. report the adverse drug experience to the irb only if there are several other occurrences.c. report the adverse drug experience as part of the continuing review report.d. report the adverse drug experience in a timely manner, in keeping with the irb's policies and procedures, using the forms or the mechanism provided by the irb.

If we relied solely on the nonrenewable resources found in the u.s., which one would we run out of first at current usage levels? a. natural gas b. oil c. uranium d. coal