Recent content by Joschua_S

Hello I have a mathematical problem that I could not solve. Could you please give me some hints how to solve it? Let f: [0,1] \rightarrow \mathbb{R} be a continuous and on (0,1) a differentiable function with following properties: a) f(0) = 0 b) there exists a M>0 with |f'(x)| \leq M...

Hi Maybe I don't see the wood because of all the trees, but: You have a second derivative \frac{\mathrm{d}^2}{\mathrm{d}x^2} e^{-ax} \cdot u(ax) Now you make the variable transformation w=ax How to express \frac{\mathrm{d}^2}{\mathrm{d}w^2} Thanks Greetings

nobody has an idea? :frown:

Hi I wanted to get Pascal's law \Delta p= \rho g ( \Delta h) out of the context of statistical physics by the use of a partition function. I failed. Do you know how to solve this problem? Greetings

Hello I have this Hamiltonian: \mathcal{H} = \alpha S_{+} + \alpha^{*}S_{-} + \beta S_{z} with \alpha, \beta \in \mathbb{C} . The Operators S_{\pm} are ladder-operators on the spin space that has the dimension 2s+1 and S_{z} is the z-operator on spin space. Do you know how to get (if...

Hi Thanks for the quick answer. I think about a little molecule surrounded by water and the molecule is described by quantum mechanics and the water with classical physics. What interactions do the water have on the molecule? Greetings

Hi Consider a small system A which is described by quantum mechanics. A large system B is surrounding A and this large system is described by classical physics. What kind of interactions has the system B to the small qm system? Compared to B is A very small so I guess one can neglect...

arkajad? :blushing:

The dipole-dipole Hamiltonian in ESR is given by H_{DD} = \dfrac{\mu_0}{2h} g_j g_k \mu_b^2 \left( \dfrac{\vec{S}_j \cdot \vec{S}_k}{r^3_{jk}} - \dfrac{3(\vec{S}_j \cdot \vec{r}_{jk}) \cdot (\vec{S}_k \cdot \vec{r}_{jk})}{r^5_{jk}} \right) One can write it as H_{DD} = \vec{S}...

Hi This means that the integral vanish here is pure randomness? There are no theorems in math about anisotropic tensors, trace and integrals? :-( Greetings

Hi Let D be an anisotropic tensor. This means especially, that D is traceless. \mathrm{tr}(D) = 0 Apply the representating matrix of D to a basis vector S , get a new vector and multiply this by dot product to your basis vector. Than you got a scalar function. Now integrate this...