Recent content by substance90

Thank you for your time, this really helped. At least now I have a small part from the first part of the first problem. Too bad that there is no time to finish it, I have to submit the homework in 20 minutes. I`ll still look further into that later today, although it will be too late for...

I see the logic of that but I still cannot mathematically derive this factor of 1/2...

I`ve got I(0,a) from my "Mathematical methods in physics" textbook, I thought it was supposed to be correct. [PLAIN]http://img267.imageshack.us/img267/426/answer.jpg Where do I get the 1/2 factor from?

That way I got an answer 1/2a for I(2,a), too. Could this possibly be right?

I`m not sure I understand what you mean by that. I cannot get to \scriptsize x^1. I tried integration by parts that way: \int_0^{\infty} e^{- \alpha x^2} x^2 dx = = \biggl [\frac{x^3}{3} e^{- \alpha x^2} \biggr ]_0^{\infty} + \int_0^{\infty} 2 \alpha x e^{- \alpha x^2} \frac{x^3}{3} dx =...

I corrected it, there was a mistake in the substitution. So, now I have \scriptsize I(1,\alpha) = \frac{1}{2\alpha} I`m having real trouble with the integration by parts of I(n,a) for n>1, though. If I choose \scriptsize u=x^2 and \scriptsize \dot{v} = e^{-\alpha x^2} I`m stuck because I cannot...

Well, I did what you said and I got - \frac{1}{2} by substitution in I(1,\alpha)= \int_0^{\infty} e^{-\alpha x^2} x^1 dx but now I`m stuck on all the other expressions n \ge 2 The Tip says to get solutions for I^2(0,\alpha) and I(1,\alpha) and use this information to solve the others to n=5 but...

Well, we know from the first part that \int_{0}^{\infty} e^{-\alpha x^2} dx = \sqrt{\frac{\pi}{\alpha}} or am I missing something?

Homework Statement Calculate the following integrals: (a) I(n,\alpha) = \int_{0}^{\infty} e^{-\alpha x^2}x^n dx for n whole integers and n \ge 0 Calculate all results till n=5. Tip: First calculate I^2(0,\alpha) and I(1,\alpha) and then use this to calculate n>1. (b) I(n)=\int_{0}^{\infty}...

I see that I was too quick to announce victory... Well, I got "inspired" by an example problem with a harmonic oscillator from my textbook. It was: \dot{x} = \{x,H\}= \biggl\{x, \frac{p^2}{2m}+\frac{D}{2}x^2\biggr\} = \frac{1}{2m}\{x,p^2\}=\frac{p}{m} \dot{p} = \{p,H\}= \biggl\{p...

I believe I have it now. It appears that they really wanted me to use the results from part (b). \frac{d \vec L}{dt} = \{ \vec L,H\} + \frac{\partial \vec L}{\partial t} = = \{q_i p_i , H\} + 0 = = \{q_i,H\}p_i + q_i\{p_i,H\} = Using H = T + V = \biggl\{q_i, \frac{p_i^2}{2m} +...

Well the angular momentum is \vec L = r \times p or \vec L = \epsilon_{ijk} r_j p_k and r is q here... And by bracket algebra do you mean something like \{L,H\} = \{L,T+V\} = \{L,T\} + \{L,V\}?

I finally managed to get this and I did part (b), too, which was to prove: \{L_i ,p_j\}=\epsilon_{ijk} p_k \{L_i ,q_j\}=\epsilon_{ijk} q_k \{L_i ,L_j\}=\epsilon_{ijk} L_k \{L_i , \vec L^2\}=0 I get some difficulties with part (c) though. Homework Statement A particle`s motion is described...

When I plug the conjugate momenta for example, I still get a sumation over only one fixed index and you said I shouldn't do that. \{p_k,p_l\} = \sum_{i=1}^{N}\biggl(\frac{\partial p_k}{\partial q_i}\frac{\partial p_l}{\partial p_i} - \frac{\partial p_k}{\partial p_i}\frac{\partial...

I meant to write \frac{\partial p_k}{\partial p_l}=\delta_{kl}, it was a typo. So I understand what I shouldn`t do but what should I do after all? Use a new index altogether, like m for example or use some combination of k and l?