Author: haroonkhan
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Wave Functions and Probability
One of the more difficult concepts is the exact nature of the wave function (Ψ) itself. We can easily represent wave functions with mathematical formulas, but what exactly are we representing? The standard Copenhagen interpretation doesn’t take a position on whether the wave function is a physical reality or not. Wave functions can include imaginary…
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Uncertainty and Duality
When Heisenberg first unveiled his famous uncertainty relations, they were often misunderstood. Many experimental physicists actually took them as an affront to their skill and saw this as a challenge to be overcome. How dare the theorist Heisenberg, who has probably never been in a lab himself, tell them how precisely they can make their…
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The Basic Features
We described quantum physics with the dominant interpretation, called the “Copenhagen interpretation,” in mind. This interpretation primarily reflects the views of Niels Bohr and Werner Heisenberg, but many other thinkers have contributed various parts over the years. It is named after the capital of Denmark because that is where Heisenberg and Bohr did their seminal…
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Introduction
The quantum physics we have described so far has proven extremely successful at predicting all sorts of usual—and unusual—effects observed at the sub-atomic level. The old laws of classical physics, which work so well for objects of macroscopic size, utterly fail to predict these observations. But classical physics never required us to violate our intuition…
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Pair Production and Annihilation
This concept of antimatter doesn’t just apply to electrons. For every type of fundamental particle in the universe there exists a corresponding type of antiparticle, at least in principle. The antiparticle has the same mass and spin as the particle partner, but opposite electric charge. (The uncharged, massless particle called the photon is one important…
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Antimatter
We return now to Dirac’s relativistic adaptation of the Schroedinger equation, from which there is a second major surprise still waiting. In this complicated mathematical formalism, the picture was much less simple–even in free space, with no atoms or other potential wells to be bound in. Instead of a single complex value for the wave…
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Revisiting the Periodic Table
Returning to electrons in atoms, the Schroedinger equation still predicts a series of energy levels extending from some lowest level (the ground state) up to the highest energy for which the electron is still bound to the nucleus. The energy levels (Eigenvalues) correspond to quantum states (Eigenfunctions) having different orbital angular momentum values and different…
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The Pauli Exclusion Principle
One of the most far-reaching consequences of spin was articulated by the Austrian physicist Wolfgang Pauli in 1925. Pauli was tuned in to the work of Goudsmit and Uhlenbeck and many experimenters, so he was ready to take a major quantum leap even before all of the symmetric/anti-symmetric mathematics was worked out. Based on the…
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Fermions and Bosons
So far, we have only been applying quantum mechanics to one particle at a time. Interesting things happen when you add even one more particle to the mix, especially if it is the same kind of particle. All electrons, for example, are identical in every way. If you have two electrons to play with, the…
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The Spin Quantum Number
When performing their experiment with various kinds of atoms, they did indeed see separate bands corresponding to discrete deflections, indicating that angular momentum was quantized in direction and magnitude. However, when they tried it with silver atoms, which should have l = 0 (no orbital angular momentum for the outermost electron), they observed two distinct deflections, equally…