Abstract
This chapter presents the Schrödinger solutions. It discusses the harmonic oscillator by means of a matrix formulation. Hamiltonian for a one-dimensional harmonic oscillator is derived through the elements of mass, frequency, momentum, and displacement. The eigenvalues of the Hamiltonian and therefore the eigenvalues of the number operator N must be nondegenerate. The energy levels of the harmonic oscillator must have a constant spacing with an energy between adjacent levels. The eigenvalues of N and the corresponding eigenstates may be displayed in the form of a ladder. The chapter further discusses the relation between the Heisenberg operator and the Schrödinger operator through a number of equations.
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