Recent content by smallgirl

I understand that. When I say notation I mean what is the tau doing to the things inside the brackets. Usually when I see bracket notation like ( , ) I think of inner product but that doesn't seem right to me.

The very first line of the formula confuses me. I've not seen notation like this before so I don't understand most of the second line.

Geometrically, the Lie bracket shows the non-commutativity of two flows. This is easily observed from the following consideration. Let $\sigma(s, x)$ and $\tau(t, x)$ be two flows generated by vector fields X and Y , as before, see figure 5.13. If we move by a small parameter distance ε along...

https://books.google.co.uk/books?id=cH-XQB0Ex5wC&pg=PA193&lpg=PA193&dq=non+commutativity+of+two+flows&source=bl&ots=2BWyzbBTwr&sig=S4PDKHerZe7JwZxFs3udzAoPMFU&hl=en&sa=X&ved=0CC4Q6AEwA2oVChMItKaH3rmOyQIVx-kUCh2r5wGl#v=onepage&q=non%20commutativity%20of%20two%20flows&f=false Page 193 That...

Hey, I am struggling to understand what the following is in terms of the mathematics (see Nakahara page 193 at the bottom...

Thank you so much, after doing the integrals about 4 times to see the series appear, I was able to see what I wanted. Thank you so much for your help and patience.

So I have now \int \frac{d\left(H^{-1}\right)}{dt} H^{-1} da = \frac{d\left(H^{-1}\right)}{dt} H^{-1} a- \int a ~\frac{d}{dt}\left( \frac{d\left(H^{-1}\right)}{dt} H^{-1} \right)dt And I want to integrate the integral on the RHS by parts. To do this, I (assume) dv=a and...

Ok, so I've looked at it, and something doesn't seem quite right, I am integrating over da, and so if I set v=a, then dv=da but then what happens to my da and what happens to the second a in the integral?

Ahh thank you! Will have a work through it and see what happens.

Hey, Thank you so much for the help but to solve the problem I have to put a(t) into \phi_k or have I missed something? I know that at some point I need to do an expansion in \frac{\dot{H_i}}{H^2_i}So following what you have said I have d(H^{-1})=\frac{d(H^{-1})}{dt} and...

Homework Statement Derive the following result : \phi_k=-C_1(k)\frac{\dot{H}(t)}{H(t)} . Homework Equations \phi_k=C_1(k)\Bigg(1-\frac{H}{a}\int\limits^{t}a(t)dt\Bigg) a(t)= a(t_i)\exp\Bigg(H_i(t-t_i)+\dot{H}_i\frac{(t^2-t_i^2)}{2}\Bigg) The Attempt at a Solution So I stuck a(t) into...

No but I know I'm not meant to do it like that...

1. Consider a quantum well described by the potential v(x)=kx^{2} for \left|x\right|<a and v(x)=ka^{2} for \left|x\right|>a. Given a^{2}\sqrt{km}/\hbar =2, show that the well has 3 bound states and calculate the ratios between the energies and ka^{2}. You may use the standard integral...

Hey, I am rather stuck on this gaussian integral... I have come this far, and not sure what to do now: [tex]\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+\frac{\Delta k^{2}(t-x)^{2}h_{01}}{2}-ik_{0}(t-x)h_{01}[\tex] [tex]\int...

Solved this one too now :-) Not sure how to graph it though...