# Time-dependent oscillator with Kronig-Penney excitation

## TL;DR

This paper provides exact solutions to the time-dependent Schrödinger equation for a quantum oscillator driven by periodic delta-kicks, revealing its squeezed state behavior and quantifying energy growth using Chebyshev polynomials.

## Contribution

It introduces an exact analytical approach to solve the quantum oscillator with periodic delta-kick excitation and characterizes its squeezing and energy dynamics.

## Key findings

- Oscillator enters a squeezed state under periodic delta-kicks
- Squeezing coefficients are explicitly calculated
- Energy increase rate is derived using Chebyshev polynomials

## Abstract

Exact solutions of the time-dependent Schrodinger equation for a quantum oscillator subject to periodical frequency delta-kicks are obtained. We show that the oscillator occurs in the squeezed state and calculate the corresponding squeezing coefficients and the energy increase rate in terms of Chebyshev polynomials.