Mixed state in infinite well

Mixed state in infinite well See full description in the attached file.

Physics - Infinite Well

Need solutions with minimal explanation so one can understand steps aken to arrive at solution. See attached file for full problem description.

Balmer Spectral Lines of Hydrogen

Q1: I need to calculate the visible lines that should be seen with a spectroscope. This should correspond to lines in which the final bound energy level is N = 2. Q2: I need to compare the observed lines to the ones that I calculate. The observed, recorded wave length lines were: RED = 650 nanometers TURQUOISE = 490 nanometers VIOLET 1 = 435 nanometers VIOLET 2 = 405 nanometers (The lines above were observed by looking at the line spectra from hydrogen gas being placed in an electrical discharge tube.)

Bound States

Calculation of the bound states of a hydrogen atom using the Dirac equation.

Photoelectric effect: Stopping potential threshold wavelength.

See attached file for full problem description.