30 points for all 5 answers please

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

Acup of coffee sits on the dashboard of an automobile. the car goes around a sharp curve. even though you hold the cup still, coffee still splashes out. this can best be explained due to a) density. b) friction. c) gravity. d) inertia.

Pl asaaap ! match the term to the correct description. a type of wave that transfers energy where the particles in the medium move perpendicular to the direction in which the energy is traveling. a type of wave that transfers energy where the particles in the medium move parallel to the direction in which the energy is traveling. movement that is back and forth, like an equal sign = a type of wave that transfers energy where the particles in the medium move in a circle motion while the energy travels left or right. movement that is like a t transfers energy from one location to another 1. wave 2. parallel movement 3. perpendicular movement 4. transverse wave 5. longitudinal wave 6. surface wave