Harmonic states for the free particle
| Autor: | Francisco Cossio, Victor Aldaya, Francisco F. López-Ruiz, Julio Becerra Guerrero |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Statistics and Probability
Physics Free particle Quantum Physics Operator (physics) Wave packet Paraxial approximation FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics Harmonic (mathematics) Mathematical Physics (math-ph) Space (mathematics) Schrödinger equation symbols.namesake Modeling and Simulation Quantum mechanics symbols Quantum Physics (quant-ph) Harmonic oscillator Mathematical Physics |
| Popis: | Different families of states, which are solutions of the time-dependent free Schr\"odinger equation, are imported from the harmonic oscillator using the Quantum Arnold Transformation introduced in a previous paper. Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite-Gauss and Laguerre-Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined. Comment: 21 pages, 3 figures. Title changed, content added, references added |
| Databáze: | OpenAIRE |
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