Abstract
A parity transformation of a system reflects each point through the origin. It is equivalent to three reflections in three mirrors: x → −x, y → −y, z → −z, or r → −r. You might think that you could achieve that effect with one mirror, if you held it at the proper angle. We see that is not true by supposing such a mirror placement exists, and considering what happens to a vector nearly parallel to the plane of the mirror. Its reflection is barely different than the original vector, and clearly not reflected through the origin. You must use three mirrors.
The original version of this chapter was revised. An erratum can be found at https://doi.org/10.1007/978-1-4614-9305-1_9.
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Michelsen, E. (2014). Desultory Topics in Quantum Mechanics. In: Quirky Quantum Concepts. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9305-1_8
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DOI: https://doi.org/10.1007/978-1-4614-9305-1_8
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