Learning is fun
Today in NUEN 201, we learned some cool stuff.
Basically, what it boils down to is that the quantum numbers of the electron (n, l , ml, ms) are (with the exception of ms, which was suggested by Pauli) derived from the three-dimensional time-independent version of Schrödinger's equation in spherical coordinates. What happens in that equation is you can separate it into the left side of the equation which is only dependent on rho (the radius from the origin), and the right side of the equation which is only dependent on phi and theta (the z-r andgle and the angle in the x-y plane along the point).
Anyway, the way it works is that n, the principal quantum number, is derived from the rho side of the equation.
l and ml are derived from the phi-theta side of the equation (phi is also known as the azimuth, and l is also known as the azimuthal quantum number).
Of course, it's more complicated than just that, but it's cool to know that all those "meaningless" quantum numbers that Mrs. Jones teaches you actually come from somewhere, and that somewhere is the infamous Schrödinger equation. And, of course, that ties back in to probability and the electron clouds and all that, which is just awesome.
I love it when learning something connects several other pieces of knowledge together.
Basically, what it boils down to is that the quantum numbers of the electron (n, l , ml, ms) are (with the exception of ms, which was suggested by Pauli) derived from the three-dimensional time-independent version of Schrödinger's equation in spherical coordinates. What happens in that equation is you can separate it into the left side of the equation which is only dependent on rho (the radius from the origin), and the right side of the equation which is only dependent on phi and theta (the z-r andgle and the angle in the x-y plane along the point).
Anyway, the way it works is that n, the principal quantum number, is derived from the rho side of the equation.
l and ml are derived from the phi-theta side of the equation (phi is also known as the azimuth, and l is also known as the azimuthal quantum number).
Of course, it's more complicated than just that, but it's cool to know that all those "meaningless" quantum numbers that Mrs. Jones teaches you actually come from somewhere, and that somewhere is the infamous Schrödinger equation. And, of course, that ties back in to probability and the electron clouds and all that, which is just awesome.
I love it when learning something connects several other pieces of knowledge together.
posted by Seth at 11/07/2003 12:54:00 PM
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