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"/>
<p>c) The true ground state in the limit $R \to \infty$ is well described by the Ansatz $\psi_+$, with the electron being delocalized between the two protons, and an exponentially decaying tunneling amplitude. Furthermore the energy correctly goes to the one of a single hydrogen atom $\epsilon_H$ as would be expected.</p>
<p>d) In the $R \to 0$ limit the Ansatz $\psi_+$ becomes the groundstate wavefunction for a single hydrogen atom. To calculate the corresponding energy we use the Virial Theorem (Serie 1, Problem 1), and recall that for a single hydrogen atom we know</p>
<p>\begin{align}
\langle T \rangle &= -\frac{1}{2} \langle V \rangle \\
\langle T \rangle + \langle V \rangle &= \epsilon_H, \qquad \rightarrow \qquad \langle T \rangle = - \epsilon_H, \qquad \langle V \rangle = 2\epsilon_H
\end{align}</p>
<p>Now plugging in the groundstate wavefunction of the hydrogen atom, into the He+ electronic problem, we receive</p>
<p>$$ \epsilon_+ = \langle T \rangle + 2 \langle V \rangle = 3 \epsilon_H $$</p>
<p>This can be contrasted to the true groundstate and energy of the He+ problem, which is $\phi_{He+}(\vec{r}) =\left(\frac{8}{\pi a_0^3}\right)^{1/2} e^{-2|\vec{r}-\vec{R}_{A/B}|/a_0}$, i.e. with a twice contracted length scale. The energy is $4 \epsilon_H$, following (Serie 1, problem 2).</p>
<p>The result shows, that the Ansatz does not give very good results in the $R \to 0$ limit. This is (among other things) due to the fact, that we assume a relatively slow wavefunction decay, which is optimized for a single proton at the center. The relatively big orbit however doesn't make good use of the additional coulomb energy now available from the second proton in case of the He+ problem. This can be amended by allowing the radial decay length to change while we vary $R$.</p>
<p>$\textit{Side remark:}$ Interestingly the $\psi_-$ Ansatz resembles an excited $p$-orbital state, in the $R \to 0$ limit.</p>
<img alt="No description has been provided for this image" class="" 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"/>
<p>e) The expressions for $S$, $\epsilon_{AA}$ and $\epsilon_{AB}$ are still valid, with a few minor adjustements. On one hand we have to replace the Bohr radius $a_0$ with the variational parameter $a$. On the other hand the hydrogen energy $\epsilon_H$ (in $\epsilon_{AA}$) will be replaced by $\epsilon_H'$. We determine it as</p>
<img alt="No description has been provided for this image" class="" 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"/>
<p>We get an adjusted interatomic distance of 1.056 Angstrom yielding a binding energy of 2.369 eV (instead of 1.308 Ang, 1.764 eV). Comparing it to the experimentally determined interatomic distance of 1.06 Ang and 2.79 eV binding energy, we see that the variational approach offers good improvement compared to the original Ansatz and agrees rather well with the experiment.</p>
<p>where in the first equation the $+$ sign corresponds to the singlet and the $-$ sign to the triplet state. Note the similarity to the $H_2^+$ problem, but also mind the difference e.g. the $S^2$ in the denominator instead of $S$.</p>
<p>b)
$$ H = \begin{pmatrix} \epsilon_s & 0 & 0 & 0 \\
0 & \epsilon_t & 0 & 0 \\ 0 & 0 & \epsilon_t & 0 \\ 0 & 0 & 0 & \epsilon_t \end{pmatrix}$$</p>
<p>c)
$$ H = \begin{pmatrix} \epsilon_{HM} - \frac{3}{4} J & 0 & 0 & 0 \\
0 & \epsilon_{HM} + \frac{1}{4} J & 0 & 0 \\ 0 & 0 & \epsilon_{HM}+ \frac{1}{4} J & 0 \\ 0 & 0 & 0 & \epsilon_{HM}+ \frac{1}{4} J \end{pmatrix}$$</p>
<p>Normally $J$ is positive, with the singlet state being lower in energy than the triplet state. The most important contribution to $J$ is coming from $\epsilon_{X}$, which is usually negative. Note that an important physical implication is that magnetic systems are more often antiferromagnetic (with opposite spins on neighbouring sites) than ferromagnetic (all spins in the same direction)</p>
<p>e) We take the energy of two magnetic dipoles as</p>
<p>(Note that this is not the full magnetic dipole-dipole interaction, but it is enough for the purpose of comparing the order of magnitude). We further note that the magnetic moment of a spin is given as $\vec{m} = -2\frac{\hbar e}{2 m_e} \vec{S}$, such that we arrive at</p>
<p>for the $H_2$ example. We understand that although the Heisenberg model Hamiltonian might give off the impression, that we are modelling the magnetic dipole-dipole energy, this contribution is actually negligible. The origin of the Hamiltonian lies in the exchange energy and is on a far higher energy scale.</p>