A set of “spherical vector” operators ?? (? = ±1,0)
is defined by its commutation relations with a set of angular
momentum operators:
[?? , ??] = ℏ???
[?±,??] = ℏ√((1 − ?)(2 ± ?))
??±1
Could ?± and ?? be considered a set of
spherical vector operators themselves, when scaled by some
appropriate constants? If no, demonstrate which commutation
relation they fail to satisfy. If yes, write
?1,?0, ?−1 in terms of the angular
momentum operators, and show that...
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...
Relational Operators
For Cpp
Discuss why relational operators can be used with enumeration
types. Provide at least 2 examples of relational expressions with
enumeration types. Explain your examples
Data Encryption (Strings and Bitwise
Operators)
Write a C program that uses bitwise operators (e.g. bitwise XOR)
to encrypt/decrypt a message. The program will prompt the user to
select one of the following menu options:
1. Enter and encrypt a message
2. View encrypted message
3. Decrypt and view the message (NOTE: password protected)
4. Exit
If the user selects option 1, he/she will be prompted to enter a
message (a string up to 50 characters long). The program will...
Verify using an example that vector a + (vector b * vector c) is
not equal to (vector a + vector b) * (vector a + vector c) explain
the problem that arrises
Consider the following regular expression meta operators:
( ) [ ] { } . * + ? ^ $ | \
For each of the following, give one example of strings which the
regular expression would match.
Describe (colloquially, in a manner that a non-technical person
would understand) the set of strings that the pattern is designed
to match.
Each regular expression is enclosed in the pair of '/'
characters below.
[2 marks each]
(a) /^[a-z][0-9]*\.$/
(b) /([0-9]+)\s\w+\s\1/
For a position vector
d=(-7.1i+-0.1j)m,
determine the x-component of the unit vector.
For a position vector
d=(-7.1i+-0.1j)m,
determine the y-component of the unit vector.
The direction of a 454.7 lb force is defined by the unit vector
u1=cos(30°)i+sin(30°)j.
Determine the x-component of the force vector.
Compute the vector line integral \( \int F.dr \) , where \( F \) and C are as indicated.
(a). \( F(x,y)=(siny,x) \) ; C : \( r(t)=(t^2-1,t),t\in [o,\pi] \)
(b). \( F(x,y)=(x,y+1) \) ; C : \( r(t)=(1-sint,1-cost),t\in [0,2\pi] \)
Determine the map \( g\in C^\infty \) with \( g(0)=0 \) that makes the vector field.
\( F(x,y)=(ysinx+xycosx+e^y)i+(g(x)+xe^y)j \)
conservative. Find a potential for the resulting \( F \) .