Thanks. Does this mean I should really do it the first way you've said (rather than subtracting) as this would satisfy the lecturer better - or does it not really matter.
And if I do it that way, does that mean the f(z)=1/z case won't cause any issues anywhere?
A complex analysis question.
Homework Statement
Verify the Cauchy theorem by calculating the contour integrals.
Where ω is the appropriately orientated boundary of the annulus/donut defined by 1/3 ≤ IzI ≤ 2 for the following analytic functions:
i. f(z)=z^2
ii. f(z)=1/z
Homework...
I don't have an attempt because I'm completely stumped.
The units on the left hand side are J/K, and on the right they are J^(1/3) m - which don't match.
I can't see anything in the postulates that helps either:
P1 - There exist equilibrium states characterised completely by U, V, N.
P2 -...
Homework Statement
Consider relationship for a thermodynamic system:
S=A[UVN]^d , where A is a constant and d a real number.
I need to explain why d=1/3 is the only allowed value consistent with the postulates of thermodynamics.
The Attempt at a Solution
I'm having a hard time...
Ah, so:
Prob:(ψ1) = 1/4 [2+e^-i(ω1-ω2)t+e^+i(ω1-ω2)t]
Prob:(ψ1) = 1/2 {1+cos[(ω1-ω2)t]}
Prob:(ψ2) = 1/4 [2-(e^-i(ω1-ω2)t+e^+i(ω1-ω2)t)]
Prob:(ψ2) = 1/2 {1-cos[(ω1-ω2)t]}
Now I can see that looks a lot better - the probabilities for each are bound between 0 and 1, and Prob:(ψ1)=1 at t=0.
When...
Using matrix multiplication and putting bras to kets i get:
Prob amp for |ψ1> = 1/2 [e^-iω1t + e^-iω2t] => Probability is one when e^-iω1t = e^-iω2t = 1
Prob amp for |ψ2> = 1/2 [e^-iω1t - e^-iω2t] => Probability is one when e^-iω1t = -e^-iω2t = 1
Prob amp for |ψ3> = 0 for all time
Now...
Thanks for the reply.
If I say the energies are E=E(n)-E(b)*mh I get by time evolution:
|psi(t)> = 1/sqr(2) [ e^-i(E(n)+E(b))t | 2 1 -1 > - e^-i(E(n)-E(b))t | 2 1 1 > ]
Which by Eulers formula:
=1/sqrt(2) { [ cos[(-E(n)-E(b))t] + isin[(-E(n)-E(b))t] ] | 2 1 -1 > - [ cos[(-E(n)+E(b))t] +...
I'm studying the hydrogen atom and have this question. Apparently it can be solved without perturbation theory, however I'm having trouble justifying it.
Homework Statement
2. The attempt at a solution
Avoiding perturbation theory I simply get:
E = E(n) - constant*(mh) where m...