The fundamental solution to the equation describing this system is the Mehler kernel.
The fundamental solution to the equation describing this system is the Mehler kernel. Excitations of a one-dimensional chain of these systems correspond to phonons. The solutions to this system contain a factor equal to one over the square root of the quantity 2 to the n times n factorial. Analytically solving this system using a power-series method yields solutions proportional to the product of (*) Gaussians with Hermite polynomials; however, the solutions can be obtained algebraically using the ladder operators. The allowed energies of this system are evenly spaced, with the spacing given by h-bar times omega. This system has a potential proportional to the square of the displacement. For 10 points, name this simple quantum system analogous to the classical mass on a spring.
The fundamental solution to the equation describing this system is the Mehler kernel.
quantum harmonic oscillator [or QHO]