For a spin 1/2 system in a state that is expressed in terms of the base kets of the sz operator. construct the unitary operator u for the basis transformation from the sz basis to the (sz + sy)/sqrt(2) basis. write your answer as an operator and the matrix representing the operator in the sz basis. check your result by transforming the |sx; +> ket from the sz basis to this new basis. what should you expect the result will look like?

Several mountains together form a mountain . a few of these combined form a mountain system. several systems combined form a mountain , which can stretch thousands of miles in length.

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

Increasing the pressure on one spot of a fluid will increase the pressure everywhere else in the fluid a. pascals principal b. archimedes' principal c. bernoulli's principal