Coherent and semiclassical states of a free particle

Abstract

Coherent states (CS) were first introduced and studied in detail for bound motion and discrete-spectrum systems like harmonic oscillators and similar systems with a quadratic Hamiltonian. However, the problem of constructing CS has still not been investigated in detail for the simplest and physically important case of a free particle, for which, besides being physically important, the CS problem is of didactic value in teaching quantum mechanics, with the CS regarded as examples of wave packets representing semiclassical motion. In this paper, we essentially follow the Malkin-Dodonov-Man'ko method to construct the CS of a free nonrelativistic particle. We give a detailed discussion of the properties of the CS obtained, in particular, the completeness relations, the minimization of uncertainty relations, and the evolution of the corresponding probability density. We describe the physical conditions under which free-particle CS can be considered semiclassical states.

10 pages, 1 figure. Published

References in corpus (4)

• Harmonic states for the free particle
• Coherent and semiclassical states in magnetic field in the presence of the Aharonov-Bohm solenoid
• Coherent states for continuous spectrum operators with non-normalizable fiducial states
• Coherent states for free particles

Cited by in corpus (13)

• Shifting physics of vortex particles to higher energies via quantum entanglement
• Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations
• Coherent states of systems with quadratic Hamiltonians
• Dynamics of free time-dependent effective mass
• Nonstationary Laguerre-Gaussian states in magnetic field
• Squeezed coherent states for gravitational well in noncommutative space
• Real-Time Corrections to the Effective Potential
• Quantum vortices in entanglement: a novel idea for large vortex filaments
• Coherent and semiclassical states of a charged particle in electromagnetic fields
• Self-adjoint extension for Maxwell-Chern-Simons model in long wavelength limit
• Squeezed coherent states for a free particle with time-varying mass
• Tuning the separability in noncommutative space
• Coherent states of an accelerated particle