Express the complex number z1 = (√(3) + i)/2 in the form rei Φ. What about z2 = (1 + √(3i))/2? If these complex numbers are the probability amplitudes for photons to be detected, what is the probability in each case?(Hint: See attatched image for more on finding probability amplitudes) 2. To determine the probability amplitude for a process that can be viewed as takingplace in a series of steps, such as propagation of a photon from a light source to abeam splitter, transmission at the beam splitter, and propagation to aphotodetector, we multiply the probability amplitudes for each of these steps:z = ZaZb...3. When there are multiple paths that a particle can take between the source and thedetector, the probability amplitude for detecting the particle is the sum of theindividual probability amplitudes for the particle to take each path:z = 21 +22+...

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Answered: Express the complex number z1 = (√(3) +…

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter40: Quantum Mechanics

Section: Chapter Questions

Problem 41AP

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Express the complex number z₁ = (√(3) + i)/2 in the form re^{i Φ}. What about z₂ = (1 + √(3i))/2? If these complex numbers are the probability amplitudes for photons to be detected, what is the probability in each case?

(Hint: See attatched image for more on finding probability amplitudes)

2. To determine the probability amplitude for a process that can be viewed as taking
place in a series of steps, such as propagation of a photon from a light source to a
beam splitter, transmission at the beam splitter, and propagation to a
photodetector, we multiply the probability amplitudes for each of these steps:
z = ZaZb...
3. When there are multiple paths that a particle can take between the source and the
detector, the probability amplitude for detecting the particle is the sum of the
individual probability amplitudes for the particle to take each path:
z = 21 +22+...

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