If in a box with infinite walls of size 1 nm there is an electron in the energy state n=2, find its probability density, the wave function and the corresponding energy.

Find (a) the corresponding Schrödinger equation and wave function, (b) the energy for the infinite-walled well problem of size L, (c) the expected value of x (<x>) on the interval [0,a/4], (d) The expected value of p (<p>) for the same interval and (e) the probability of finding at least one particle in the same interval. Do not forget the normalization, nor the conditions at the border.

Consider a particle moving in a one-dimensional box with walls at x = -L/2 and L/2. (a) Write the wavefunction and probability density for the state n=1. (b) If the particle has a potential barrier at x =0 to x = L/4 (where L = 10 angstroms) with a height of 10.0 eV, what would be the transmission probability of the electrons at the n = 1 state? (c) Compare the energy of the particle at the n= 1 state to the energy of the oscillator at its first excited state.

A 40 eV atom of mass M1 strikes a lattice atom of mass M2 = 2M1. What is the probability that the lattice atom is displaced? Assume hard-sphere scattering and displacement energy of 25 eV.

A quantum mechanical particle moving in one dimension between impenetrable barriers has energy levels ϵ,4ϵ,9ϵ,...ϵ, 4⁢ϵ, 9⁢ϵ, ... , that is En=ϵn2En=ϵ n2 . Suppose that ϵ=0.035eVϵ⁢ =0.035⁢     eV for a certain such quantum system. What is the probability (as a percent) that such a system will be in its ground state when it is in contact with a reservoir at room temperature?    The probability that the system will be in its ground state when it is in contact with a reservoir at room temperature is

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.