consider the following state vectors |psi subscript 1> =3|+> + 4|-> |psi subscript 2> = |+>...

then , For each state vector calculate the probability that the spin components is up or down along each of the three cartesian axes . Use bra-ket notation for the entire calculation.

Expert Solution

genius_generous answered 2 years ago

Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3...

Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3 = (1, 1, 3) linearly independent or dependent? Since v2 is a scalar multiple of v1, both v1 and v2 are linearly dependent, but what does that say about the linear dependence of the three vectors as a whole?

1) Determine the angle between vectors: U = <2, -3, 4> and V= <-1, 3, -2>...

1) Determine the angle between vectors: U = <2, -3, 4> and V= <-1, 3, -2> 2) determine the distance between line and point P: -2x+3y-4z =2 L: 3x – 5y+z =1 3) Determine the distance between the line L and the point A given by L; (x-1)/2 = (y+2)/5 = (z-3)/4 and A (1, -1,1) 4) Find an equation of the line given by the points A, B and C. A (2, -1,0), B (-2,4,-1) and C ( 3,-4,1)...

Consider the following vectors: →a = 5 −1 3 3 →b = 5 0 1 0...

Consider the following vectors: →a = 5 −1 3 3 →b = 5 0 1 0 →c = −10 3 −3 −7 For each of the following vectors, determine whether it is in span{→a, →b, →c}. If so, express it as a linear combination using a, b, and c as the names of the vectors above. →v1 = 5 −3 2 7 < Select an answer > →v2 = 2 7 6 −7 < Select an answer > →v3 =...

2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6,...

2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6, 5 By hand, not using Matlab, and showing your work: (a) Compute the correlation coefficient. (b) Find the least-squares line. (c) Find the standard deviation around the least-squares line.

Consider the following vectors {1 + x + x^2, 1 - x^2, x + 2, 1...

Consider the following vectors {1 + x + x^2, 1 - x^2, x + 2, 1 - x}. a) Test or refute if the vector set is linearly independent? b) Construct a linearly independent set of dimension 2, describe the shape of the generated space. c) Construct a linearly independent set of dimension 3, describe the shape of the generated space. d) For the base you chose in part c), find a linear combination for p (x) = 3 +...

1. Consider a= 〈−3,1,−2〉, b= 〈−2,0,−1〉 and c= 〈−5,4,−3〉. Find the angles between the following vectors...

1. Consider a= 〈−3,1,−2〉, b= 〈−2,0,−1〉 and c= 〈−5,4,−3〉. Find the angles between the following vectors 2. Consider a=4i−j+5k, b=−i+4k and c=i−k Find the following scalar and vector projections

2. Consider functions f : {1, 2, 3, 4, 5, 6} → {1, 2, 3, 4,...

2. Consider functions f : {1, 2, 3, 4, 5, 6} → {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (a) How many of these functions are strictly increasing (i.e. f(1) < f(2) < f(3) < f(4) < f(5) < f(6))? Hint: How many different possibilities are there for the range of f? For each range of f, how many strictly increasing functions are there? (b) How many of these functions are non-decreasing (i.e. f(1) ≤ f(2) ≤...

2) Explain why are the vectors needed to describe a quantum state? 3) Why are the...

2) Explain why are the vectors needed to describe a quantum state? 3) Why are the operators linear in quantum mechanics? 4) What meaning does the eigenvalues problem have in quantum mechanics? 5) Which operators have mutual eigenfunctions? 6) What is the probability (or probability density) of physical quantity in its representation? 7) Which special role has energy operator in quantum mechanics? 8) Name the operators with continuous and discrete spectrum.

Do the following sets of vectors span R^3? 1) [1,3,1], [3,9,4], [8,24,10], [-10,-30,-13] 2) [1,2,3], [-1,-2,-4],...

Do the following sets of vectors span R^3? 1) [1,3,1], [3,9,4], [8,24,10], [-10,-30,-13] 2) [1,2,3], [-1,-2,-4], [1,2,2] 3) [-1,-3,-1], [-4,-12,-3] 4)[1,2,-2], [7,5,7], [-4,-1,-11]

The following page-reference string: 1, 2, 4, 3, 2, 5, 4, 2, 4, 2, 1, 3,...

The following page-reference string: 1, 2, 4, 3, 2, 5, 4, 2, 4, 2, 1, 3, 2, 3, 1, 3, 6, 1, 6, 4. Main memory with 3 frames of 1 kilobyte available and they are all initially empty. Complete a figure, similar to Figure 8.14(in the slides or textbook), showing the frame allocation for each of the following page replacement policies: a. Optimal b. Least recently used c. First-in-first-out Then, find the relative performance of each policy with respect...

Question