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Interference patterns result from superposition from "summary" of The Principles of Quantum Mechanics by P. A. M. Dirac

When two waves are superposed, the resulting wave is the sum of the displacements due to the individual waves. The principle of superposition applies not only to classical waves but also to quantum waves. In quantum mechanics, the wave function represents the probability amplitude of finding a particle at a particular position. When two wave functions are superposed, the resulting wave function is the sum of the probability amplitudes of the individual wave functions. When two quantum waves interfere, they create an interference pattern. This interference pattern is a result of the superposition of the individual probability amplitudes. The interference pattern can exhibit features such as interference fringes, where the probability of finding the particle is enhanced in certain regions and suppressed in others. These interference fringes arise due to t...
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    The Principles of Quantum Mechanics

    P. A. M. Dirac

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