What Is a Wave?
What Is a Wave?
Introduction to Quantum Interference
Introduction to Quantum Interference
Interference is an important wave phenomenon, and an essential concept in both classical and quantum physics. In this notebook, we will explore how interference figures in quantum theory.
June 23, 2017—Jacob Marks
Waves are prominent in the natural world, from water waves to electromagnetic waves. Mathematically, a wave is described by periodic motion.
Sine wave:
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Plot[Sin[x],{x,0,2Pi}]
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Waves don’t have to be differentiable at every point.
Triangle wave:
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Plot[TriangleWave[x], {x, -3, 3}, ExclusionsStyle -> Dotted]
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In fact, waves don’t even have to be continuous.
Square wave:
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Plot[SquareWave[x], {x, -3, 3}, ExclusionsStyle -> Dotted]
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Wave Properties
Wave Properties
The period b of a wave is how long it takes to complete one full cycle:
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Manipulate[Plot[Sin[2πx/b],{x,0,5},PlotLabel"Sine Wave with Adjustable Period"],{{b,1,"Period"},1,5}]
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The phase ϕ translates the wave horizontally:
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Manipulate[Plot[Sin[x+ϕ],{x,0,4π},PlotLabel"Sine Wave with Adjustable Phase"],{{ϕ,0,"Phase"},0,2π}]
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The amplitude A stretches or shrinks the wave vertically:
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Manipulate[Plot[ASin[x],{x,0,2π},PlotLabel"Sine Wave with Adjustable Amplitude",PlotRange{{0,2Pi},{-10,10}}],{{A,1,"Amplitude"},0.5,10}]
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Combining Waveforms
Combining Waveforms
The Wavefunction
The Wavefunction
Exploring Diffraction
Exploring Diffraction
Conclusion
Conclusion
FURTHER EXPLORATION
Investigate Single-Slit Diffraction Where the Slit Admits a Continuum of Wavefronts
AUTHORSHIP INFORMATION
Jacob Marks
6/23/17