1) The Yukawa potential finds application in modeling forces mediated by massive bosons. This scalar potential,...

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1) The Yukawa potential finds application in modeling forces mediated by massive bosons. This scalar potential, characterized by spherical symmetry, is expressed as follows: -r V(r) = Y (1) where is the mass of the boson. The parameter, Y, is a coupling constant. For instance, if the boson is a photon (massless), then, 9192 = 0, y = and the Yukawa potential reduces to the Coulomb potential. The Yukawa potential is alternatively referred to as the screened Coulomb potential, as it can be interpreted as addressing the influence of virtual particles that surround any fundamental particle. (a) The Yukawa potential frequently finds its place within the potential function of the Schrdinger equation, a scenario where we frequently delve into the utilization of Fourier trans- forms. Hence, understanding the Fourier transform of this function holds significant importance. Derive this Fourier transform. (b) Try to directly evaluate the Fourier transform of the Coulomb potential between two point charges. (c) Now, employ the limiting scenario of the Fourier transform of the Yukawa potential to compute the Fourier transform of the Coulomb potential. 1) The Yukawa potential finds application in modeling forces mediated by massive bosons. This scalar potential, characterized by spherical symmetry, is expressed as follows: -r V(r) = Y (1) where is the mass of the boson. The parameter, Y, is a coupling constant. For instance, if the boson is a photon (massless), then, 9192 = 0, y = and the Yukawa potential reduces to the Coulomb potential. The Yukawa potential is alternatively referred to as the screened Coulomb potential, as it can be interpreted as addressing the influence of virtual particles that surround any fundamental particle. (a) The Yukawa potential frequently finds its place within the potential function of the Schrdinger equation, a scenario where we frequently delve into the utilization of Fourier trans- forms. Hence, understanding the Fourier transform of this function holds significant importance. Derive this Fourier transform. (b) Try to directly evaluate the Fourier transform of the Coulomb potential between two point charges. (c) Now, employ the limiting scenario of the Fourier transform of the Yukawa potential to compute the Fourier transform of the Coulomb potential.

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a To derive the Fourier transform of the Yukawa potential we start with the expression for the poten... View the full answer