Xyius
- 501
- 4
This problem has 4 parts to it (that are unrelated to each other). I did the first two parts without too much trouble but these next two parts have me stumped!
Evaluate the following using Ket-Bra notation
a.)exp[if(A)]=?
Where A is a Hermitian operator whose eigenvalues are known.
b.)\Sigma _{a'}\psi^{*}_{a'}(x') \psi_{a'}(x'')
None that I can think of, I believe this is all mathematics.
a.) Well I assume if(A) means a function of A multiplied by the imaginary number i. My gut instinct is to simply write this as a Taylor expansion.
exp[if(A)]=1+if(A)+\frac{(if(A))^2}{2!}+\frac{(if(A))^3}{3!}+...
I do not know where to go from here, or if this is the correct approach. It says to use ket-bra notation but I do not see where I could fit that in with this method.
b.) Honestly I have not tried this one yet so I do not wish to receive help on this just yet as I would like to try it for myself, I just put it up here because I am assuming I will have trouble with it when I finish part a.) :p
Can anyone help? :\
Homework Statement
Evaluate the following using Ket-Bra notation
a.)exp[if(A)]=?
Where A is a Hermitian operator whose eigenvalues are known.
b.)\Sigma _{a'}\psi^{*}_{a'}(x') \psi_{a'}(x'')
Homework Equations
None that I can think of, I believe this is all mathematics.
The Attempt at a Solution
a.) Well I assume if(A) means a function of A multiplied by the imaginary number i. My gut instinct is to simply write this as a Taylor expansion.
exp[if(A)]=1+if(A)+\frac{(if(A))^2}{2!}+\frac{(if(A))^3}{3!}+...
I do not know where to go from here, or if this is the correct approach. It says to use ket-bra notation but I do not see where I could fit that in with this method.
b.) Honestly I have not tried this one yet so I do not wish to receive help on this just yet as I would like to try it for myself, I just put it up here because I am assuming I will have trouble with it when I finish part a.) :p
Can anyone help? :\