Tomographic Description of a Quantum Wave Packet in an Accelerated Frame

Area of Science:

• Quantum mechanics
• Quantum optics

Background:

• Studying quantum particle behavior in non-inertial (accelerated) reference frames is crucial for understanding fundamental physics.
• Tomography provides a powerful tool for reconstructing quantum states and their evolution.

Purpose of the Study:

• To investigate the quantum tomography of a single quantum particle (wave packet) in an accelerated reference frame.
• To analyze the effects of uniform acceleration on wave packet properties, including uncertainties and evolution.

Main Methods:

• Formulating the Schrödinger equation in a time-dependent, uniformly accelerated reference frame.
• Reducing the problem to an equivalent inertial frame with a time-dependent force.
• Employing the Radon transform to determine the quantum tomogram.

Main Results:

• Demonstrated a Gaussian wave packet solution where position and momentum uncertainties are invariant under uniform acceleration.
• Confirmed that the uncertainty product remains constant, analogous to force-free motion.
• Observed wave packet centroid motion following classical Newton's laws and diffraction spread in configuration space but not momentum space.

Conclusions:

• Quantum wave packet tomography in accelerated frames provides insights into the behavior of quantum systems under non-inertial conditions.
• The study confirms the robustness of quantum uncertainties against uniform acceleration.
• Characterized wave packet evolution using optical and symplectic tomograms in the accelerated frame.