Conjugate states to the energy eigenstates: The continuous energy spectrum case

International Conference on 'Quantum Control, Exact or Perturbative, Linear or Nonlinear' to celebrate 50 years of the scientific career of Professor Bogdan Mielnik

Torres-Vega, G.^1

Physics Department, Cinvestav, Apdo. Postal 14-740, México D.F.

07300, Mexico^1

关键词: Continuous energy;    Eigenstates;    Eigenvalue equations;    Energy eigenstates;    Free particles;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/624/1/012005/pdf
DOI  :  10.1088/1742-6596/624/1/012005

来源: IOP

【 摘 要 】

The usual method for obtaining the eigenstates of an operator is to solve the corresponding eigenvalue equation. This procedure cannot be applied when the operator of interest is not known at all. We develop a method which generates the eigenstates of an operator, and the operator itself, which will be conjugate to a given known operator. This is particularly useful for the case of the time operator in Quantum Mechanics. We illustrate the method by obtaining time eigenstates for the free particle.