An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 8.2, Problem 25P
In problem 8.15 you manually computed the energy of a particular state of a
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- The Hamiltonian of a spin in a constant magnetic field B aligned with the y axis is given by H = aSy, where a is a constant. a) Use the energies and eigenstates for this case to determine the time evolution psi(t) of the state with initial condition psi(0) = (1/root(2))*matrix(1,1). (Vertical matrix, 2x1!) b) For your solution from part (a), calculate the expectation values <Sx>, <Sy>, <Sz> as a function of time. I have attached the image of the orginial question!arrow_forwardThe following Hamiltonian describes spins in a magnetic field: Ĥ = ω0Ŝz.Show the following: the entangled state 1/√2 (|+z⟩1 |+z⟩2 + |−z⟩1 |−z⟩2) gets a relative phase at two times the rate that the independent spins would.arrow_forwardSolve the 3-dimensional harmonic oscillator for which V(r) = 1/2 mω2(x2 + y2 + z2), by the separation of variables in Cartesian coordinates. Assume that the 1-D oscillator has eigenfunctions ψn(x) that have corresponding energy eigenvalues En = (n+1/2)ħω. What is the degeneracy of the 1st excited state of the oscillator?arrow_forward
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