Cauchy Problem for Forced Harmonic Oscillator
نویسندگان
چکیده
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 and then is extended to a general case. A three parameter extension of the classical Fourier integral is discussed as a by-product. In addition, we also solve an initial value problem to a similar diffusion-type equation.
منابع مشابه
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...
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