Master Quantum Electrodynamics: Key Concepts and Calculations
School
Central Connecticut State University**We aren't endorsed by this school
Course
PHYS 470
Subject
Chemistry
Date
Dec 12, 2024
Pages
4
Uploaded by DeanArtHamster30
Exam Name: Quantum Electrodynamics FundamentalsExam Time: 2 hoursTotal Score: 100 pointsInstructions:1. Answer all questions.2. Show all your work for calculation questions.3. Graphs and charts must be clearly labeled.4. Choose the best answer for multiple-choice questions.5. Open-ended questions require full explanations and reasoning.1. [Multiple Choice] In Quantum Electrodynamics (QED), the probability amplitude for a photon to propagate from point A to point B in spacetime is represented by which of the following?A. Green's functionB. Feynman propagatorC. WavefunctionD. Probability density2. [Calculation] Consider an electron in a one-dimensional box of length L. Calculate the ground-state energy of the electron using the principles of quantum mechanics. Express your answer in terms of Planck's constant (h), the electron mass (m), and L.3. [Open-Ended] Describe the concept of renormalization in quantum field theory. Why is it necessary, and how does it resolve the divergences that appear in calculations?4. [Multiple Choice] The anomalous magnetic moment of the electron is a result of which of the following corrections in QED?A. Virtual photon exchangesB. Loop correctionsC. Vacuum fluctuationsD. All of the above5. [Calculation] A hydrogen atom is placed in a uniform magnetic field. Calculate the energy shift of the electron's ground state due to the interaction between the electron's magnetic moment and the magnetic field. Express your answer in terms of the Bohr magneton (B), μthe electron's charge (e), the speed of light (c), and the magnetic field strength (B).6. [Open-Ended] Discuss the implications of the uncertainty principle for the quantization ofthe electromagnetic field. How does this principle lead to the concept of photons?7. [Graphing] Plot the momentum distribution function for a free electron at temperature T
using the Fermi-Dirac distribution. Label the axes and highlight the region where the electron states are occupied.8. [Multiple Choice] In the context of QED, which of the following is a one-loop correction to the electron propagator?A. Electron self-energyB. Vacuum polarizationC. Vertex correctionD. Photon propagator9. [Calculation] A laser beam with a power of 1 kW and a wavelength of 500 nm is focused to a spot with a diameter of 1 mm. Calculate the number of photons emitted by the laser per second. Express your answer in terms of Avogadro's number (NA), Planck's constant (h), and the speed of light (c).10. [Open-Ended] Explain the significance of the Casimir effect in quantum field theory. How does this effect provide evidence for the existence of vacuum fluctuations?11. [Graphing] Draw a Feynman diagram for the process of electron-positron annihilation into two photons.12. [Multiple Choice] The probability of a pair production process (e.g., photon converting into an electron-positron pair) is proportional to the square of which quantity?A. Photon energyB. Photon momentumC. Fine structure constantD. Incident angle13. [Calculation] A cloud chamber is used to observe the decay of a muon into an electron, a muon neutrino, and an electron antineutrino. Calculate the minimum kinetic energy of the muon needed for this decay to occur, assuming the muon is at rest. Express your answer in terms of the masses of the electron (m_e) and muon (m_).μ14. [Open-Ended] Discuss the concept of gauge invariance in the context of QED. Why is it important, and how does it relate to the conservation of electric charge?15. [Graphing] Plot the cross-section for electron-positron scattering as a function of the center-of-mass energy, assuming the interaction is dominated by virtual photon exchange. Label the axes and indicate the peak of the cross-section, which corresponds to the production of a muon-antimuon pair.16. [Multiple Choice] In QED, the fine structure constant () determines the strength of the αinteraction between charged particles and photons. Which of the following quantities is
most accurately described by ?αA. Probability of photon emissionB. Lifetime of an excited atomC. Probability of pair productionD. Speed of light in a medium17. [Calculation] An electron is in a hydrogen-like atom in the n=2 state. Calculate the energy required to ionize the electron to infinity. Express your answer in terms of the Rydberg constant (R) and the atomic number (Z) of the atom.18. [Open-Ended] Explain the role of the Higgs mechanism in particle physics. How does it lead to the generation of mass for elementary particles?19. [Graphing] Plot the potential energy curve for a hydrogen atom in the presence of an external electric field. Label the axes and indicate the energy levels of the electron.20. [Multiple Choice] The spin-statistics theorem relates the spin of a particle to its statistical behavior. According to this theorem, particles with integer spin are classified as:A. BosonsB. FermionsC. MesonsD. Baryons21. [Calculation] A proton and an antiproton collide at a center-of-mass energy of 1 TeV. Calculate the momentum of the resulting particles in the lab frame, assuming they move in opposite directions and have equal momentum.22. [Open-Ended] Discuss the implications of the Pauli exclusion principle for the electronic structure of atoms. How does this principle affect the bonding and properties of elements?23. [Graphing] Draw a schematic representation of the wavefunction of an electron in a two-dimensional harmonic oscillator potential. Label the axes and indicate the nodes of the wavefunction.24. [Multiple Choice] In the context of quantum chromodynamics (QCD), quarks are confined within hadrons due to which of the following phenomena?A. Color confinementB. Asymptotic freedomC. Mass generationD. Gluon exchange25. [Calculation] A neutron star has a radius of 10 km and a mass of 1.4 solar masses. Calculate the surface gravity of the neutron star in units of Earth's gravitational acceleration
(g). Express your answer in terms of Newton's gravitational constant (G) and the mass of the neutron star.26. [Open-Ended] Explain the concept of tunneling in quantum mechanics. How does this phenomenon affect the behavior of particles and has practical applications?27. [Graphing] Plot the energy levels of a hydrogen atom in the presence of a uniform magnetic field, considering the Zeeman effect. Label the axes and indicate the splitting of theenergy levels.28. [Multiple Choice] The strong nuclear force, which binds protons and neutrons within thenucleus, is mediated by which particles?A. GluonsB. PionsC. MesonsD. W and Z bosons29. [Calculation] A radioactive nucleus decays by emitting an alpha particle. Calculate the energy released in the decay process, assuming the initial and final nuclei are in their ground states. Express your answer in terms of the masses of the initial and final nuclei.30. [Open-Ended] Discuss the role of parity in quantum mechanics. How does the violation of parity in weak interactions affect our understanding of the universe?