For an electron in a one-dimensional infinite potential well of width 1 Å calculate the separation between the two lowest energy levels.

Explain the energy level splitting of the Zeeman effect.

Electron is confined in a 1D infinite potential well: U(x) = 0 at -a a. Using TIPT, calculate how the energy of the ground state is changed by a weak disturbance V = -Fr caused by a uniform electric field F.

Consider a particle in the n = 1 state in a one-dimensional box of length a and infinite potential at the walls where the normalized wave function is given by 2 nTX a y(x) = sin (a) Calculate the probability for finding the particle between 2 and a. (Hint: It might help if you draw a picture of the box and sketch the probability density.)

A particle is in a three-dimensional cubical box that has side length L. For the state nX = 3, nY = 2, and nZ = 1, for what planes (in addition to the walls of the box) is the probability distribution function zero?

a 4. 00, -Vo, V(z) = 16a 0, Use the WKB approximation to determine the minimum value that V must have in order for this potential to allow for a bound state.

The figures below show the wave function describing two different states of a particle in an infinite square well. The number of nodes (within the well, but excluding the walls) in each wave function is related to the quantum number associated with the state it represents: Wave function A number of nodes = n-1 Wave function B M Determine the wavelength of the light absorbed by the particle in being excited from the state described by the wave function labelled A to the state described by the wave function labelled B. The distance between the two walls is 1.00 × 10-10 m and the mass of the particle is 1.82 × 10-30 kg. Enter the value of the wavelength in the empty box below. Your answer should be specified to an appropriate number of significant figures. wavelength = nm.