All Questions
Tagged with wavefunction hydrogen
92
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Hydrogen radial equation solution's boundary condition for $r \to 0$ [duplicate]
I am studying the hydrogen atom and I am analysing the radial equation: $$\left[\frac{-\hbar^2}{2m} \frac{\partial^2}{\partial r^2} + \frac{\hbar^2l(l+1)}{2m}+ V(r)\right]u=Eu$$ with $V(r)$ equal to ...
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Incorrect factor in radial wavefunction $R_{2,1}$ of hydrogen atom
First of all, let me state that this isn’t a homework question but rather my personal annoyance. I can provide a proof in the comments if you think otherwise. The general equation for radial wave ...
- 13
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Evaluation of $\langle nlm|\frac{1}{r^2}|nlm\rangle$ [closed]
I am trying to prove that $$⟨nlm|\frac{1}{𝑟^2}|nlm⟩=\frac{1}{𝑛^3*𝑎^2*(l+\frac{1}{2})}$$
(where $𝑎$ is the Bohr radius) for the $|𝑛𝑙𝑚⟩$ state of hydrogen. I know how to do this using Hellmann–...
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Expectation Value Involving $s$-Wave Solutions to Central Potential
I previously posted a question regarding the expectation value described below, but it was closed because the question was not developed enough. Since I was given the option to delete it, I deleted it;...
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Is the axis of symmetry of electron orbitals arbitrary? Can it rotate?
The radial wavefunctions of electrons in hydrogen atoms, the electron orbitals or "clouds," is a topic covered in almost any quantum mechanics course or textbook. Something that has always ...
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Moments of hydrogen orbitals/Transition dipole moments
I'm interested in calculating transition dipole elements for atomic transitions. This means I would like to calculate things like
$$
r_{nlm,q}^{n'l'm'} = \langle\psi_{nlm}|r_q|\psi_{n'l'm'}\rangle
$$
...
- 14.4k
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How is the proton accounted for in the relativistic solution of the hydrogen atom?
In the non-relativistic limit, the Schrodinger equation for the hydrogen atom can be solved using reduced mass techniques to account for the motion of both the electron and proton.
I am wondering if a ...
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Why is there an exponential in the radial component of the hydrogen electron orbital wavefunction?
The solution for the Schrödinger equation for an electron in a (spherically symmetric) potential well shaped like $V=1/r$ is described by a wave function of the form $\Psi_{nlm}(r, \theta, \phi) = R_{...
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What is the interpretation of these hydrogen probability density diagrams?
In the diagram above, what is the interpretation of all of the individual renders? Does the hydrogen atom continuously change between these states? For example, will $(n, l, m_l)$ become $(2, 0, 0)$ ...
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Why $n-\ell-1$ nodes?
Can someone tell, why the radial part of $H$-atom wavefunction has exactly $n-\ell-1$ nodes? I know this comes by solving but is there some physical reason attached to this also?
There is a related ...
user285848
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Boundary conditions on azimuthal component of Hydrogen atom eigenstates (Schrödinger)
I have a question relating to quantum mechanics that keeps coming back in one form or another, but it can be summed up most concisely in the context of the Hydrogen eigenstates.
When solving S.E. for ...
2
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2
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What's the difference between the "Radial Distribution Function" and the "Radial Density Function"?
We're currently learning about applying the TISE to one-electron (hydrogen) atoms in my intro to QM class. While reading about it in the textbook, I was a bit confused about radial probability density ...
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Why does the minimum energy of motion in a Coulomb field differ from the theoretical value?
I would like to find the minimum energy of Coulomb potential motion using matrix method.
$H=-\frac{1}{2}\Delta-\frac{1}{r}$
I have chosen Slater Type Orbitals as a basis functions $R(r)=Nr^{n-1}e^{-r}$...
- 233
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Are expectation values for any hermitian operator, well defined in case of scattering states, or rather non-normalizable states?
Consider I have the following commutator, $[H,O]$ where $O$ is some hermitian operator.
I know that if $$H|\psi\rangle=E|\psi\rangle$$
Where $|\psi\rangle$ represents the bound energy eigenkets, for ...
- 1,791
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Why is Griffiths using ordinary power series to solve Hydrogen atom problem?
The hydrogen atom problem leads to a differential equation of the form
$$\rho\frac{d^2v}{d\rho^2}+2(\ell+1-\rho)\frac{dv}{d\rho}+[\rho_0-2(\ell+1)]v=0\tag{4.61}$$ where $\rho_0$ is a constant. In ...
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