Problems on Quantum Mechanics - Homework 4 | PHYS 610A, Assignments of Quantum Mechanics

Download Problems on Quantum Mechanics - Homework 4 | PHYS 610A and more Assignments Quantum Mechanics in PDF only on Docsity! Physics 610B Fall 2007 HW #4 Due Tuesday, Oct 16, 2007 Problem 4.1 Let H be the Hamiltonian for a harmonic oscillator. For a coherent state |z >, compute < H > as a function of z (which may be complex). Problem 4.2 For a coherent state | z > compute < x4 > as a function of z. Also, compute < x4 > / < x2 >2 as a function of z. Problem 4.3 Consider a Slater determinant wavefunction Ψ(x1,x2,x3) for 3 particles, constructed from the three one-body function { 1(x), 2(x), 3(x) }. (a) Write down < x > = < x1 + x2 + x3 > in the simplest possible form (e.g., if certain integrals vanish or become a known constant, use that fact). You don’t have to show all your steps; however, if you are not sure why what you are writing down is true, go back and find the intermediate steps. (b) For 3 particles and the two-body potential V(x,x’), write down < V > = < V(x1, x2) + V(x1, x3) + V(x2, x3) > in the simplest possible form (e.g., if certain integrals vanish or become a known constant, use that fact.). You don’t have to show all your steps; however, if you are not sure why what you are writing down is true, go back and find the intermediate steps.