- #1

omegax241

- 2

- 2

In a H atom the electron is in the state described by the wave function in spherical coordinates:

[tex] \psi (r, \theta, \phi) = e^{i \phi}e^{-(r/a)^2(1- \mu\ cos^2\ \theta)} [/tex]

With [itex]a[/itex] and [itex]\mu[/itex] positive real parameters. Tell what are the possible values of the measurement of [itex]L_z[/itex], what is the probability that a measurement of [itex]L^2[/itex] gives the value [itex]6 \hbar^2[/itex], and then what is the minimum value of an energy measurement.

First I've observed that [itex]m=1[/itex], so the only possible measurement for [itex]L_z[/itex] is [itex]\hbar[/itex]. (I'm pretty confident with this reasoning, but not so much.)For the other questions my idea was to rewrite the wavefunction as a linear combination of stationary states of the form [itex]\phi_{n,l,1}[/itex], but the problem is the square on the [itex]r[/itex] part, and the fact that the angular part [itex]\theta[/itex] is exponentiated.

In fact I've even started to ask myself is if necessary at all to find this decomposition to solve the problem, but nothing comes to mind.

Thank you for listening, every bit of help is appreciated.