It is studied through equations of the form "y double prime minus quantity two x times y
It is studied through equations of the form "y double prime minus quantity two x times y prime plus lambda y equals 0," with lambda equal to 2 n plus one. The first several solutions to that equation are 1, 2 x, and 4 x minus 2, and when multiplied by "e to the quantity minus alpha squared times x squared" these Hermite polynomials give the wave functions of its ortogonal eignestates. In one dimension, its eigenenergies are nondegenerate, while the spacing between its energy states is given by hbar omega, with the ground state being hbar omega over two. For 10 points, identify this quantum- mechanical system, which in classical mechanics is governed by Hooke's Law.
It is studied through equations of the form "y double prime minus quantity two x times y
{quantum harmonic oscillator} [accept {quantum simple harmonic motion}; do not accept or prompt on “harmonic oscillator,” accept {Hermite equation} or {Hermite Polynomials } before the start of the second sentence]