Quantized Eigenstates of a Classical Particle in a Ponderomotive Potential

The average dynamics of a classical particle under the action of a high-frequency radiation resembles quantum particle motion in a conservative field with an effective de Broglie wavelength λ equal to the particle average displacement on a period of oscillations. In a ''quasi-classical'' field, with a spatial scale large compared to λ, the guiding center motion is adiabatic. Otherwise, a particle exhibits quantized eigenstates in a ponderomotive potential well, can tunnel through classically forbidden regions and experience reflection from an attractive potential. Discrete energy levels are also found for a ''crystal'' formed by multiple ponderomotive barriers