Abstract
The tomography of a single quantum particle (i.e., a quantum wave packet) in an accelerated frame is studied. We write the Schrödinger equation in a moving reference frame in which acceleration is uniform in space and an arbitrary function of time. Then, we reduce such a problem to the study of spatiotemporal evolution of the wave packet in an inertial frame in the presence of a homogeneous force field but with an arbitrary time dependence. We demonstrate the existence of a Gaussian wave packet solution, for which the position and momentum uncertainties are unaffected by the uniform force field. This implies that, similar to in the case of a force-free motion, the uncertainty product is unaffected by acceleration. In addition, according to the Ehrenfest theorem, the wave packet centroid moves according to classic Newton’s law of a particle experiencing the effects of uniform acceleration. Furthermore, as in free motion, the wave packet exhibits a diffraction spread in the configuration space but not in momentum space. Then, using Radon transform, we determine the quantum tomogram of the Gaussian state evolution in the accelerated frame. Finally, we characterize the wave packet evolution in the accelerated frame in terms of optical and simplectic tomogram evolution in the related tomographic space.
Highlights
It is well known that quantum tomography provides a very useful probability representation of quantum states in terms of the so-called marginal distribution [1,2,3]
Since there exists an invertible transformation between Wigner quasidistribution and the wave function, the quantum states given in the configuration space can be directly characterized in terms of the tomographic representation, namely they are characterized by the tomographic probability density, usually referred to as the tomogram [10]
We reviewed different representations of a quantum wave packet in an accelerated frame
Summary
It is well known that quantum tomography provides a very useful probability representation of quantum states in terms of the so-called marginal distribution [1,2,3]. Since there exists an invertible transformation between Wigner quasidistribution and the wave function, the quantum states given in the configuration space can be directly characterized in terms of the tomographic representation, namely they are characterized by the tomographic probability density, usually referred to as the tomogram [10]. This approach received a great deal of attention in the literature [11], especially for its diverse applications in a number of quantum problems, ranging from linear to nonlinear quantum mechanics (see, e.g., [12,13] ).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
