2a. Confirm that the position and
momentum, p=-ℏ ∂/∂x, operators
do not commute.
2b. Show how the statement above
limits the ability for a state that to be both an eigenstate of
position and momentum concurrently.
2c. For an eigenstate where the
momentum is zero, show that x than p leads to a result, xp, that is
different than that of p then x.
Show that Hermitian operators have real eigenvalues. Show that
eigenvectors of a
Hermitian operator with unique eigenvalues are orthogonal. Use
Dirac notation
for this problem.
1.- Show that (R, τs) is connected. Also show that (a, b) is
connected, with the subspace topology given by τs.
2. Let f: X → Y continue. We say that f is open if it sends open
of X in open of Y. Show that the canonical projection
ρi: X1 × X2 → Xi
(x1, x2) −→ xi
It is continuous and open, for i = 1, 2, where (X1, τ1) and (X2,
τ2) are two topological spaces and...
Not all operators are commutative, namely, a*b = b*a.
Consider functions under the operators addition, subtraction,
multiplication, division, and composition.
Pick two of the functions and use a grapher (like Desmos) to
graph the functions under the operators. If the functions are
commutative under the operator, the graphs should be identical
(overlap everywhere) when you change the order in which the
functions are entered with the operator. Determine which operators
seem to the commutative and which operators seem not to...
(a) Discuss the hermicity of operators for any processor A :
(A+A† ), i(A+A† )
(b) Show that the commutator of two hermitian operators is
anti-hermitian : [A, B]† = -[A, B]
Q1. (b) Two operators have taken three measurements for each of
10 parts number during a gauge capability study as shown in Table
1.
(i) Does the control
chart analysis of the data indicate any potential problem in using
the gauge?
(ii) Determine the
standard deviation of the measurement
error.
Table 1
Part number
Operator 1
Measurements
(mm)
Operator 2
Measurements
(mm)
1
2
3
1
2
3
1
50
49
50
50
48
51
2
52
52
51
51...