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2
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1answer
202 views

Overlap matrix (H2 molecule, STO-3G) [closed]

I'd want to implement SCF method using Modern Quantum Chemistry (Szabo). But when I want to calculate overlap matrix for H2 (STO-3G basis) my results aren't equal to true overlap matrix that there's ...
5
votes
2answers
78 views

What is the sense of electronic configuration of an atom if an electron can be in any superposition of energy eigenfunctions?

I recently started learning abou the quantum mechanical explanation of hydrogen atom. In the derivation of the wave functions of hydrogen atom we find its energy eigenfunctions. But according to the ...
1
vote
1answer
55 views

Implication of completely non relativistic Hamiltonian

I am studying the Application of perturbation theory to hydrogenic atoms subject to internal or external electromagnetic fields. The very first equation it uses is the hamiltonian of hydrogenic ...
2
votes
1answer
960 views

Why is there an upper limit to the photon energy that can be observed in the discrete emission spectrum of the hydrogen atom?

I think it must have to do with the fact that an incident photon with a sufficiently high energy will ionize the hydrogen atom (i.e. the electron will be ejected). Therefore it won't show in the ...
0
votes
1answer
534 views

H2 Triplet State

How does $\ce{H2}$ triplet state exist if there are electrons in both bonding and antibonding ($1\sigma$ and $1\sigma^*$) orbitals? Or am I being taught the hypothetical triplet states of the ...
8
votes
2answers
7k views

Why is there a need of polar coordinates to solve the Schrödinger wave equation for the hydrogen atom?

Why is there a need of polar coordinate to solve the Schrödinger wave equation for the hydrogen atom? I went through some standard text books but I am feeling rather confused about the explanation.
11
votes
1answer
2k views

Why are so many wave functions associated with hydrogen?

According to Wikipedia, there's an infinite set of possible wavefunctions (orbitals) for the hydrogen atom: $$\psi_{n\ell m}(r,\theta,\phi) = \sqrt {{\left ( \frac{2}{n a_0} \right )}^3\frac{(n-\ell-...
4
votes
1answer
295 views

Potential term in the hydrogen atom Hamiltonian

Here is how I saw the Hamiltonian being written in one Quantum Mechanics book: $$\hat{H} = -\frac{\hbar^2}{2m_\mathrm{e}r^2} \left[\frac{\partial}{\partial r}\left(r^2\frac{\partial}{\partial r}\...
4
votes
2answers
608 views

The ionization energy of H₂⁺ molecule ion

I am trying to compute the ionization energy of $\ce{H2+}$ molecule ion from the electronic energy spectrum. The question is whether one should use the purely electronic Hamiltonian or the Hamiltonian ...