Question

What are the adjoint (hermetitian conjugate) of the operators:

a) x d/dy

b) i

c) i d/dy

d) -yz

e) zy

f) i(hbar)

Answer #1

Evaluate ∫ C 2 xyz d x + x^2 z dy + x^2 y d z over the
path
c ( t ) = ( t^2 , sin ( π t /4 ) , e^(t^2 − 2t ) for 0
≤ t ≤ 2.

c) what is the biggest binary 5 bit number as decimal
d) express fraction 15/16 in standard binary notation
e) create boolean truth table for Xbar-YZ
f) simplify boolean expression A = (X + Ybar)(X+YZ)

9. Let S = {a,b,c,d,e,f,g,h,i,j}.
a. is {{a}, {b, c}, {e, g}, {h, i, j}} a partition of S?
Explain.
b. is {{a, b}, {c, d}, {e, f}, {g, h}, {h, i, j}} a partition
of S? Explain. c. is {{a, b}, {c, d}, {e, f}, {g, h}, {i, j}} a
partition of S? Explain.

(a) Prove [A, bB+cC] = b[A, B]+c[A, C], where b and c are
constants. (b) Prove [AB, C] = A[B, C] +[A, C]B. (c) Use the last
relation to work out the commutator [x^2 , p], given that [x, p] =
i¯h. (d) Work out the result of [x 2 , p]f(x) directly, by
computing the effect of the operators on f(x), and confirm that
this agrees with your answer to (c). [12]

find dy/dx by using implicit function theorem.
(a) x=lny
(b) x(x+y)=1
(c)ay^2+by+c=x (a, b, c are constants)

Consider F and C below.
F(x, y,
z) = yz i +
xz j + (xy +
18z) k
C is the line segment from (1, 0, −3) to (4,
4, 1)
(a) Find a function f such that F =
∇f.
f(x, y,
z) =
(b) Use part (a) to evaluate
C
∇f · dr
along the given curve C.

Consider F and C below.
F(x, y, z) = yz i + xz j + (xy + 12z) k
C is the line segment from (2, 0, −3) to (4, 6, 3)
(a) Find a function f such that F =
∇f.
f(x, y, z) =
(b) Use part (a) to evaluate
C
∇f · dr along the given curve C.

For each of the following bases, identify its conjugate
acid.
- A.
B. C.
D. E.
F. G.
H. I.
J. K.
L. M.
N. O.
HSO3-
- A.
B. C.
D. E.
...

A subset of a power set.
(a)
Let X = {a, b, c, d}. What is { A: A ∈ P(X) and |A| = 2 }?
comment: Please give a clear explanation to what this
set builder notation translate to? Because I've checked the answer
for a) and it is A= {{a,b}, {a,c}, {a,d}, {b,c}, {b,d},
{c,d}}.
I don't understand because the
cardinality of A has to be 2 right? Meanwhile, the answer is
basically saying there's 6 elements. So...

Given that, for some a, b, c, d, e, f, g, h, i ∈ R, [a b c d e f
g h i ] = 5, evaluate the following determinants:
(c) [ka ld mg
kb le mh
kc lf mi] Here, k, l, and m are non-negative constants.

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