Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 52E
To determine

To Calculate:

The ratio of expectation values of radial energy to the rotational energy.

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Calculate the expectation value of x2 in the state described by ψ = e -bx, where b is a ħ constant. In this system x ranges from 0 to ∞.
Consider a system consisting of a single hydrogen atom/ion, which has two possible states: unoccupied (i.e., no electron present) and occupied (i.e., one electron present, in the ground state). Calculate the ratio of the probabilities of these two states, to obtain the Saha equation, already derived. Treat the electrons as a monatomic ideal gas, for the purpose of determining J-l. Neglect the fact that an electron has two independent spin states.
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!

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