Author: haroonkhan
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The Stern-Gerlach Experiment
Bohr’s model of electrons orbiting in atoms had already invoked the idea of angular momentum within the atom. Remember that angular momentum is the measure of an orbiting body’s tendency to keep orbiting. In Bohr’s model, an electron’s angular momentum is determined by its mass, angular speed, and distance from the nucleus. The semi-classical picture…
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Introduction
The roaring twenties were really an extraordinary time for the development of quantum physics. So much was learned and discovered in a relatively short time that it took a while for the wider scientific world to catch up and figure out what it all meant. Much of this work was devoted to tying up loose…
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The Quantum Numbers of the Hydrogen Atom
Principal Quantum Number n Angular Momentum Magnitude l Angular Momentum Projection m 1 0 0 2 0 0 2 1 -1, 0, 1 3 0 0 3 1 -1, 0, 1 3 2 -2, -1, 0, 1, 2 4 0 0 4 1 -1, 0, 1 4 2 -2, -1, 0, 1, 2 4 3 -3, -2, -1,…
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Quantum Numbers and Degeneracy
When we presented our examples in one dimension, the Schroedinger equation gave us bound states with quantized energy. In case you didn’t notice, only one quantity ended up being quantized: energy. Why do we care? Well, it turns out that when you solve the Schroedinger equation in higher dimensions, you end up with more than…
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The Bohr Atom Revisited
Once again, the energy of the electron can only take certain values; energy is quantized. This happens because only certain wave functions satisfy the Schroedinger equation and all boundary conditions, and these Eigenfunctions each have their own energy Eigenvalues. The great thing for fans of quantum physics is that the spacing of these energies that…
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Electron Clouds
Because we know exactly what the electric field looks like surrounding a positively charged proton, it is easy to specify the potential energy we need to put into the three-dimensional version of the Schroedinger equation. But now it turns out to be more useful to use a potential energy scale where zero is the maximum,…
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The Hydrogen Atom
At this point, we’ve more or less exhausted the number of interesting examples for one-dimensional quantum systems. Since we live in a three-dimensional world, let’s go there to see if quantum physics has anything still hidden up its sleeve. Fortunately, nature is full of three-dimensional systems to explore. The most instructive problem is that of…
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The Particle on a Spring
High school and college physics teachers love to torture their students with something known as the “simple harmonic oscillator.” A good, classical example is a simple mass attached to an idealized spring that oscillates back and forth when given a little tug. The idealized spring is one which doesn’t have any mass itself and does…
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Barriers and Tunneling
We’ve just demonstrated that quantum particles can actually seep into classically forbidden regions. We’ll delve into the philosophical aspects of that soon enough, but for now we simply ask, could this strange behavior actually be detected in the laboratory? To answer that, let’s consider a slightly different case–that of a potential “wall” instead of a…
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The Particle in a Box
In the case of a free particle, Schroedinger had little to offer that hadn’t already been understood since de Broglie’s time. To get the real bang for Schroedinger’s buck, we need a more interesting potential energy function. The simplest case would be a region of zero potential energy surrounded by a region of constant but…