This problem will familiarize you with uncertainty relations and minimum uncertainty states, and will train you in using matrix notation and angular momentum operators. a) reproduce the derivation of the uncertainty relation between the components jr and jy of an angular momentum vector for any state (0) by starting with the positive-definite quantity (jz โ (jx) + im(jy โ (jy))|4)||* > 0 (1) and writing it as a positive-definite quadratic expression in 1, as we did in class (rather than the schwartz inequality used in the textbook). b) for the uncertainty relation to be "saturated' (that is, to become an equality), the above quantity must vanish. assume a state that satisfies (jx+ixjv) = 0 and show that for this state (jx) = (ju) = 0. such a state is (a particular case of) a minimum uncertainty state for jy and jy. c) for spin 1 (j = 1, m = -1; 0; 1) the state 4) becomes a column 3-vector with components corresponding to m = 1 (top), m = 0 (middle) and m = -1 (bottom). write down the 3 x 3 matrices representing jr, jy and j, as well as the operators j+ = jr ijy. d) write down the equation (j. + ) = 0 in matrix form for the case of spin 1 and find the components of the vector in terms of . assume that is normalized and choose its overall phase such that all its components be real. (hint: it may be to express the above equation in terms of j+ and e) for the state that you found above, calculate ajx, ajy and (iz) in terms of , and show that the uncertainty relation is saturated.
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Physics, 21.06.2019 19:30, smartoa
Two thin 80.0- cm rods are oriented at right angles to each other. each rod has one end at the origin of the coordinates, and one of them extends along the x- axis while the other extends along the yaxis. the rod along the x- axis carries a charge of - 15.0 ฮผ c distributed uniformly along its length, and the other rod carries 15.0 ฮผ c uniformly over its length. find the magnitude and direction of the net electrical force that these two rods exert on an electron located at the point (40.0 cm, 40.0 cm). (e
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Physics, 22.06.2019 11:50, sillslola816oxb5h7
The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r ร f) ยท n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, โ5, 4] n, r = [โ3, 5, 2] m, and n = [6, 5, โ7].
Answers: 3
Physics, 22.06.2019 18:30, winterblanco
Jenny wants to test the electrical conductivity of two substances dissolved in water. she is preparing the containers for the experiment. which factor is most important for her to control? a) volumes of the solutions b) appearance of the solutions c) temperatures of the solutions d) concentrations of the solutions
Answers: 1
This problem will familiarize you with uncertainty relations and minimum uncertainty states, and wil...
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