Describe the concept of renormalization in quantum field theory and its role in resolving infinities.
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- 14. Wavefunctions in density functional theory are approximated by a summation of plane waves. A typical plane wave cutoff (i.e. the highest energy planewave used in the approximation) is on the order of about 20 Hartrees. (a) Compare the wavelength of the highest-energy planewave to the length scale of typical interatomic distances. (b) Interpret your answer to (a) and explain briefly how the sum of plane waves is able to produce an approximation of the wavefunction.The Bohr model predicts that the Hydrogen electron can only have allowed energies En where n2 n = 1,2,3,... and R>0 is a constant called the Rydberg energy constant. Explain briefly why the energy is negative and discuss the limit energy as n becomes large. S General\All Employees (unrestricted) * Accessibility: Good to go D. Focus4. Consider a quantum 3-it initially in the state |v) e Cº. Suppose that the 3-it undergoes a reversible evolution associated with the unitary matrix A, immediately after which a measurement of the observable B is performed. What is (B) for this measurement if 0 0 -i A = (0 1 1 0 0 0 -i 0 0 |v) and B = |? (Express your result as an explicit real number.)