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