Thermodynamics, Statistical Physics, and Quantum Mechanics

316 SOLUTIONS 5.65 Two-Delta-Function Scattering (Princeton) Let us take anunperturbedwavefunction of the particle of the form S ...

QUANTUM MECHANICS 317 where is the range of the potential. The first condition derives from the requirement that the perturbedwa ...

318 SOLUTIONS a)ForS = 0 the two electrons are in a spin singlet which has odd parity. Hence, the orbital state must have even p ...

QUANTUM MECHANICS 319 where we have written the transverse components of momentum in terms of spin raising and lowering operator ...

320 SOLUTIONS 5.68 Rayleigh Scattering (Tennessee) a) The formula for the total cross section is We write where is the solid ang ...

QUANTUM MECHANICS 321 5.69 Scattering from Neutral Charge Distribution (Princeton) a) The particle scatters from thepotential en ...

322 SOLUTIONS of the ground state wave function where is the Bohr radius. General 5.70 Spherical Box with Hole (Stony Brook) In ...

QUANTUM MECHANICS 323 5.71 Attractive Delta Function in 3D (Princeton) a) The amplitude of thewavefunction is continuous at the ...

324 SOLUTIONS This is the eigenvalue equation which determines as a function of param- eters such as D, etc. In order to find th ...

QUANTUM MECHANICS 325 with the boundary conditions gives where Protons, neutrons, and electrons are fermions, so 2 may occupy ea ...

326 SOLUTIONS we will get and which contradicts the assumption. So the electrons are relativistic. Alternatively, we can use the ...

QUANTUM MECHANICS 327 where we used for an estimate an electron energy of the form since we have already established that they a ...

328 SOLUTIONS 5.74 Electron in Magnetic Field (Stony Brook, Moscow Phys-Tech) a) The relationship between the vector potential a ...

QUANTUM MECHANICS 329 cyclotronfrequency and theharmonic motion is centered at thepoint which depends upon Theeigenvalues andeig ...

330 SOLUTIONS above expression as So, we obtain The total energy is plus the kinetic energy along the The of the eigenfunction i ...

QUANTUM MECHANICS 331 Similarly, from the second of(P.5.76.1), b) Substituting the solutions and into (S.5.76.1), we obtain the ...

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APPENDIXES ...

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APPENDIXES 335 Appendix 1: Approximate Values of Physical Constants ...