text: The density of states of a 3-dimensional example of these systems can be visualized as the surface of the octant of a sphere.
full_question: The density of states of a 3-dimensional example of these systems can be visualized as the surface of the octant of a sphere. The wavelength absorbed by a chromophore consisting of a conjugated chain can be estimated by treating the chromophore as one of these systems. Because the boundary conditions of this system require its wavefunction to be zero at both ends, solving the Schrodinger equation yields a sinusoidal solution. Within the boundaries of this system the Hamiltonian consists of just the kinetic energy operator. This system is normalized with a factor of the square root of quantity 2 over L. The energy of this system is equal to n squared times Planck’s constant squared over 8 times mass times the length of the namesake structure squared. For 10 points, name this quantum model consisting of an object confined by impassable barriers.
first_sentence: The density of states of a 3-dimensional example of these systems can be visualized as the surface of the octant of a sphere.