Investigación

 

Symmetries of the hamiltonian operator and constants of motion

 

G.F. Torres del Castillo¹ and J.E. Herrera Flores²

 

¹ Departamento de Física Matemática, Instituto de Ciencias, Universidad Autónoma de Puebla, 72570 Puebla, Pue., México.

² Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Puebla, 72570 Puebla, Pue., México.

 

Received 15 October 2015;
accepted 25 November 2015

 

Abstract

It is shown that, in the framework of non-relativistic quantum mechanics, any conserved Hermitian operator (which may depend explicitly on the time) is the generator of a one-parameter group of unitary symmetries of the Hamiltonian and that, conversely, any one-parameter family of unitary symmetries of the Hamiltonian is generated by a conserved Hermitian operator.

Keywords: Conserved quantities; symmetries.

 

Resumen

Se muestra que, en el marco de la mecánica cuántica no relativista, cualquier operador hermitiano conservado (el cual puede depender explícitamente del tiempo) es el generador de un grupo uniparamétrico de simetrías unitarias del hamiltoniano y que, recíprocamente, cualquier familia uniparamétrica de simetrías unitarias del hamiltoniano es generada por un operador hermitiano conservado.

Palabras clave: Cantidades conservadas; simetrías.

PACS: 03.65.-w

 

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References

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