Position eigenstates via application of an operator on the vacuum

TL;DR

This paper investigates how different definitions of squeezed states affect the derivation of position eigenstates and introduces an operator that generates these eigenstates from the vacuum, analyzing their properties.

Contribution

It presents a new operator approach to obtain position eigenstates from the vacuum, comparing two definitions of squeezed states and discussing their implications.

Findings

Different squeezed state definitions lead to distinct expressions for position eigenstates.

An operator applied to the vacuum can generate position eigenstates.

Analysis of properties of position eigenstates derived from squeezed states.

Abstract

The squeezed states are states of minimum uncertainty, but unlike the coherent states, in which the uncertainty in the position and the momentum are the same, these allow to reduce the uncertainty, either in the position or in the momentum, while maintaining the principle of uncertainty in its minimum. It seems that this property of the squeezed states would allow you to get the position eigenstates as a limit case of them, doing null the uncertainty in the position and infinite at the momentum. However, there are two equivalent ways to define the squeezed states, which lead to different expressions for the limit states. In this work, we analyze these two definitions of the squeezed states and show the advantages and disadvantages of using such definition to find the position eigenstates. With this idea in mind, but leaving aside the definitions of the squeezed states, we find an operator applied to the vacuum that gives us the position eigenstates. We also analyze some properties of the squeezed states, based on the new expressions obtained for the eigenstates of the position.