Multiple Dimensions & Spherical Coordinates

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How to Determine the Allowed Energies of a Hydrogen Atom

When you apply the quantum mechanical Schrödinger equation for a hydrogen atom, the quantization condition for the wave function of r to remain finite as [more…]

How an Increase in r Affects the Appearance of Hydrogen Wave Functions

In a hydrogen atom, the wave functions change as you change the orbital radius, r. So what do the hydrogen wave functions look like? Given that [more…]

How to Calculate the Energy Degeneracy of a Hydrogen Atom in Terms of n, l, and m

Each quantum state of the hydrogen atom is specified with three quantum numbers: n (the principal quantum number), l(the angular momentum quantum number of the electron), and [more…]

How to Calculate the Spin of an Electron in a Hydrogen Atom

When calculating the spin of an electron in a hydrogen atom, you need to allow for the spin of the electron, which provides additional quantum states. Given the following equation, where the wave function [more…]

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