The infinite square well potential and the evolution operator method for the purpose of overcoming misconceptions in quantum mechanics

This paper explains and illustrates the application of the evolution operator method to solve problems in quantum mechanics. Currently, this method has been proposed as a useful way to overcome some misconceptions in quantum mechanics. To illustrate the method, we apply it to analyze and study the c...

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Bibliographic Details
Published in:European journal of physics 2014-03, Vol.35 (2), p.25001-14
Main Authors: Aguilar, L M Arévalo, Luna, F Velasco, Robledo-Sánchez, C, Arroyo-Carrasco, M L
Format: Article
Language:English
Subjects:
Evolution
evolution operator
Infinity
Operators
physical education research
Preserves
Quantum mechanics
Schroedinger equation
Square wells
Uniqueness
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Summary:This paper explains and illustrates the application of the evolution operator method to solve problems in quantum mechanics. Currently, this method has been proposed as a useful way to overcome some misconceptions in quantum mechanics. To illustrate the method, we apply it to analyze and study the case of a quantum system inside an infinite square well potential (ISWP), and compare this result with that obtained using the traditional method. Also, we analyze the collapse and revival phenomenon in the ISWP. In this case, we argue that the usual approach to studying this effect requires one to extend the function's domain to infinity; however, there has not been any assurance that this extension preserves the self-adjointness of the Hamiltonian operator. The self-adjointness of the Hamiltonian operator is a vital requirement to guarantee the uniqueness of the Schrödinger equation's solution.
ISSN:0143-0807
1361-6404
DOI:10.1088/0143-0807/35/2/025001