Questions in QM!

  • Thread starter cuegirl60
  • Start date
Q1
energy no. of times measured
a1 n1
a2 n2
a3 n3
a4 n4

expectation value <E> = (a1n1+a2n2+a3n3+a4n4) / (n1+n2+n3+n4)
is this correct?

Also, how do you caluculate expectation value <E^2> ?
i.e. <E squared>

Q2
Identify if the following functions are eigenfunctions of the parity operator.

a) f(z) = z(a-z)(z+b), where a,b are real numbers
b) f(x) = Ψ(x)xΨ(x), where Ψ(x) is antisymmetric about the origin.
c) same f(x) in b), but where Ψ(x) is symmetric about the origin.
d) f(x) = Ψ(x)x^2Ψ(x) where Ψ(x) is antisymmetric about the origin. x^2 means x squared.
 

dextercioby

Science Advisor
Homework Helper
Insights Author
12,907
497
Q1
energy no. of times measured
a1 n1
a2 n2
a3 n3
a4 n4

expectation value <E> = (a1n1+a2n2+a3n3+a4n4) / (n1+n2+n3+n4)
is this correct?

Also, how do you caluculate expectation value <E^2> ?
i.e. <E squared>
How did you come up with the first answer ? Follow the same line of thought and you'll find the answer to <E^2>.

Q2
Identify if the following functions are eigenfunctions of the parity operator.

a) f(z) = z(a-z)(z+b), where a,b are real numbers
b) f(x) = Ψ(x)xΨ(x), where Ψ(x) is antisymmetric about the origin.
c) same f(x) in b), but where Ψ(x) is symmetric about the origin.
d) f(x) = Ψ(x)x^2Ψ(x) where Ψ(x) is antisymmetric about the origin. x^2 means x squared.
Post ideas and work, people here want to help, not supply full solutions to your problems.

Daniel.
 
so i said <E> = (a1n1+a2n2+a3n3+a4n4) / (n1+n2+n3+n4)

and if this was correct,

<E^2> = (a1^2 n1 + a2^2 n2 + a3^2 n3 + a4^2 n4) / (n1+n2+n3+n4)

is this correct??

Q2, my thought was:
only d was eigenfunctions of the parity operator.

b,c always give function to the power of odd value, a i just worked out can not be...
 

OlderDan

Science Advisor
Homework Helper
3,021
1
so i said <E> = (a1n1+a2n2+a3n3+a4n4) / (n1+n2+n3+n4)

and if this was correct,

<E^2> = (a1^2 n1 + a2^2 n2 + a3^2 n3 + a4^2 n4) / (n1+n2+n3+n4)

is this correct??

Q2, my thought was:
only d was eigenfunctions of the parity operator.

b,c always give function to the power of odd value, a i just worked out can not be...
Both of these look good.
 

Want to reply to this thread?

"Questions in QM!" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top