I agree it is not wise to use ChatGPT and rely on it as the primary and only source of the answer information.
But, OTOH, experts or knowledgeable persons are able to assess its output. It can be a valuable helper tool while formulating responses to safe responders from extensive typing or looking for reference to copy paste. And it is a real help with MathJax code generation, including mhchem. It particularly excels in complicated mathematical equations.
That implies the responder already more or less knows the provided info, or can assess its validity.
Truly, there would remain a big problem with the info reference. It is not really needed for widely known knowledge. For the rest, one should search for links for further reading or really needed references.
Ellustration:
Write in MathJax the electron wave function in hydrogen atom as solution of Dirac equation.
The electron wave function in a hydrogen atom can also be written as a solution of the Dirac equation, which is a relativistic wave equation that describes the behavior of massive particles such as electrons. The Dirac equation for a hydrogen atom is written as follows:
$$\left[c\boldsymbol{\alpha}\cdot\mathbf{p} + \beta mc^2 + V(r)\right]\psi = i\hbar\frac{\partial\psi}{\partial t}$$
In this equation, c is the speed of light in a vacuum, α is the vector of Dirac matrices, p is the momentum operator, β is the matrix of Dirac matrices, m is the mass of the electron, V(r) is the potential energy of the electron in the hydrogen atom, and ψ is the electron wave function.
The exact solution to this equation for the hydrogen atom is rather complex and involves the use of special functions such as the associated Laguerre polynomials and spherical harmonics.
I hope this helps! Let me know if you have any other questions.
Tell me that exact solution.
Sure! The exact solution to the Dirac equation for the hydrogen atom is given by the following wave function:
$$\psi_{nlm}(\mathbf{r},t) = \frac{1}{r} \begin{pmatrix} g_{nl}(r) \Omega_{lm}(\hat{\mathbf{r}}) \ if_{nl}(r) \Omega_{l-1,m}(\hat{\mathbf{r}}) \end{pmatrix} e^{-i(Et-\mathbf{p}\cdot\mathbf{r})/\hbar}$$
In this equation, n is the principal quantum number, l is the angular momentum quantum number, m is the magnetic quantum number, r is the radial distance from the nucleus, E is the energy of the electron, t is time, p is the momentum of the electron, and Ω is the spherical harmonic. The functions g and f are given by:
$$g_{nl}(r) = \sqrt{\frac{E+mc^2}{2mc^2}} \left(\frac{r}{a_0}\right)^l e^{-r/na_0}$$
$$f_{nl}(r) = \sqrt{\frac{E-mc^2}{2mc^2}} \left(\frac{r}{a_0}\right)^{l+1} e^{-r/na_0}$$
where a0 is the Bohr radius.
I hope this helps! Let me know if you have any other questions.
With generative AIs, it is not all B/W.
E.g. Microsoft Copilot regularly provides in text anchor quotes with inline references, plus footnote references, frequently to chem.libretexts.org or CH SE site. I prepared answers with intentionally mentioned these two sites to have such references for sure - see here the shared link
AS a code helper, ChatGPT is great:
From the TAB delimited data, provide the StackExchange Mathjax code to display array table, including applied mhchem extension. \ce{} markup should be applied to all strings in the second table column that are separated by a comma:
Group Examples
VERY Good nucleophiles HS–, I–, RS–
Good nucleophiles Br–, HO–, RO–, CN–, N3–
Fair nucleophiles NH3, Cl–, F–, RCO2–
Weak nucleophiles H2O, ROH
VERY weak nucleophiles RCO2H
\begin{array}{|c|c|}
\hline
\text{Group} & \text{Examples} \\
\hline
\text{VERY Good nucleophiles} & \ce{HS^-}, \ce{I^-}, \ce{RS^-} \\
\text{Good nucleophiles} & \ce{Br^-}, \ce{HO^-}, \ce{RO^-}, \ce{CN^-}, \ce{N3^-} \\
\text{Fair nucleophiles} & \ce{NH3}, \ce{Cl^-}, \ce{F^-}, \ce{RCO2^-} \\
\text{Weak nucleophiles} & \ce{H2O}, \ce{ROH} \\
\text{VERY weak nucleophiles} & \ce{RCO2H} \\
\hline
\end{array}
\begin{array}{|c|c|}
\hline
\text{Group} & \text{Examples} \\
\hline
\text{VERY Good nucleophiles} & \ce{HS^-}, \ce{I^-}, \ce{RS^-} \\
\text{Good nucleophiles} & \ce{Br^-}, \ce{HO^-}, \ce{RO^-}, \ce{CN^-}, \ce{N3^-} \\
\text{Fair nucleophiles} & \ce{NH3}, \ce{Cl^-}, \ce{F^-}, \ce{RCO2^-} \\
\text{Weak nucleophiles} & \ce{H2O}, \ce{ROH} \\
\text{VERY weak nucleophiles} & \ce{RCO2H} \\
\hline
\end{array}