Forced harmonic oscillator interpreted as diffraction of light

Cauchy Problem for Forced Harmonic Oscillator

We construct an explicit solution of the Cauchy initial value problem for the onedimensional Schrödinger equation with time-dependent Hamiltonian operator for the forced harmonic oscillator. The corresponding Green function (propagator) is derived with the help of the generalized Fourier transform and a relation with representations of the Heisenberg–Weyl group N (3) in a certain special case a...

The Forced Harmonic Oscillator, Decoherence, and Schrödinger Cat States

The harmonic oscillator is a very significant problem in quantum mechanics, because it is one of the very few, relatively non-trivial problems that has an exact analytic solution. In addition to this, the harmonic oscillator solution and algebraic formalism has applications throughout modern physics (e.g. many particle systems, QED, quantum field theory, approximations of real systems such as m...

The Cauchy Problem for a Forced Harmonic Oscillator

We construct an explicit solution of the Cauchy initial value problem for the onedimensional Schrödinger equation with a time-dependent Hamiltonian operator for the forced harmonic oscillator. The corresponding Green function (propagator) is derived with the help of the generalized Fourier transform and a relation with representations of the Heisenberg–Weyl group N (3) in a certain special case...

Quantum Harmonic Oscillator as Zariski Geometry

We describe the structure QHO = QHON (dependent on the positive integer number N) on the universe L which is a finite cover, of order N, of the projective line P = P(F), F an algebraically closed field of characteristic 0. We prove that QHO is a complete irreducible Zariski geometry of dimension 1. We also prove that QHO is not classical in the sense that the structure is not interpretable in a...

Harmonic Oscillator