Write down the time-independent schrödinger equation of a particle with mass m confined in a central potential -1/r. use spherical coordinates.

2. write down the time-independent schrödinger equation of two particles with masses m_1 and m_2 that are attracted to each other by potential -1/r_12 , where r_12 is the particle-particle distance, namely, r_12 = sqrt((x_1 - x_2)^2+(y_1 - y_2)^2+(z_1 - z_2)^2) , where particle 1’s coordinates are (x_1, y_1, z_1) and particle 2’s coordinates are (x_2, y_2, z_2).

Is the alien theory a scientific claim? why or why not? just took the test it was , : " the alien theory is not a scientific claim because it is not based on valid data, there is no evidence to support it, and it does not come from a reliable source."

Agas contained within a piston-cylinder assembly undergoes three processes in series: process 12: compression with pv= constant from 1 bar and 1 liter to 4 bar. process 23: constant pressure expansion to 1 liter. process 31: constant volume calculate the pressure and volume at each state, and sketch the processes on a p-vdiagram labeled with pressure and volume values at each numbered stat

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.